Volume
LIPIcs, Volume 92
28th International Symposium on Algorithms and Computation (ISAAC 2017)
-
Part of:
Series:
Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Symposium on Algorithms and Computation (ISAAC)
Event
ISAAC 2017, December 9-12, 2017, Phuket, ThailandEditors
Publication Details
- published at: 2017-12-07
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-054-5
- DBLP: db/conf/isaac/isaac2017
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Document
Complete Volume
LIPIcs, Volume 92, ISAAC'17, Complete Volume
Abstract
LIPIcs, Volume 92, ISAAC'17, Complete Volume
Cite as
28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@Proceedings{okamoto_et_al:LIPIcs.ISAAC.2017,
title = {{LIPIcs, Volume 92, ISAAC'17, Complete Volume}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017},
URN = {urn:nbn:de:0030-drops-82924},
doi = {10.4230/LIPIcs.ISAAC.2017},
annote = {Keywords: Data Structures, Theory of Computation, Mathematics of Computing, Computing Methodologies}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, External Reviewers
Abstract
Front Matter, Table of Contents, Preface, External Reviewers
Cite as
28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{okamoto_et_al:LIPIcs.ISAAC.2017.0,
author = {Okamoto, Yoshio and Tokuyama, Takeshi},
title = {{Front Matter, Table of Contents, Preface, External Reviewers}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {0:i--0:xvi},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.0},
URN = {urn:nbn:de:0030-drops-82084},
doi = {10.4230/LIPIcs.ISAAC.2017.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, External Reviewers}
}
Document
Weighted Linear Matroid Parity
Abstract
The matroid parity (or matroid matching) problem, introduced as a common generalization of matching and matroid intersection problems, is so general that it requires an exponential number of oracle calls. Nevertheless, Lovasz (1978) showed that this problem admits a min-max formula and a polynomial algorithm for linearly represented matroids. Since then efficient algorithms have been developed for the linear matroid parity problem.
This talk presents a recently developed polynomial-time algorithm for the weighted linear matroid parity problem. The algorithm builds on a polynomial matrix formulation using Pfaffian and adopts a primal-dual approach based on the augmenting path algorithm of Gabow and Stallmann (1986) for the unweighted problem.
Cite as
Satoru Iwata. Weighted Linear Matroid Parity. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 1:1-1:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{iwata:LIPIcs.ISAAC.2017.1,
author = {Iwata, Satoru},
title = {{Weighted Linear Matroid Parity}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {1:1--1:5},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.1},
URN = {urn:nbn:de:0030-drops-82738},
doi = {10.4230/LIPIcs.ISAAC.2017.1},
annote = {Keywords: Matroid, matching, Pfaffian, polynomial-time algorithm}
}
Document
Computational Philosophy: On Fairness in Automated Decision Making
Abstract
As more and more of our lives are taken over by automated decision making systems (whether it be for hiring, college admissions, criminal justice or loans), we have begun to ask whether these systems are making decisions that humans would consider fair, or non-discriminatory. The problem is that notions of fairness, discrimination, transparency and accountability are concepts in society and the law that have no obvious formal analog.
But our algorithms speak the language of mathematics. And so if we want to encode our beliefs into automated decision systems, we must formalize them precisely, while still capturing the natural imprecision and ambiguity in these ideas.
In this talk, I'll survey the new field of fairness, accountability and transparency in computer science. I'll focus on how we formalize these notions, how they connect to traditional notions in theoretical computer science, and even describe some impossibility results that arise from this formalization. I'll conclude with some open questions.
Cite as
Suresh Venkatasubramanian. Computational Philosophy: On Fairness in Automated Decision Making. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{venkatasubramanian:LIPIcs.ISAAC.2017.2,
author = {Venkatasubramanian, Suresh},
title = {{Computational Philosophy: On Fairness in Automated Decision Making}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {2:1--2:1},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.2},
URN = {urn:nbn:de:0030-drops-82747},
doi = {10.4230/LIPIcs.ISAAC.2017.2},
annote = {Keywords: fairness, transparency, accountability, impossibility results}
}
Document
Faster Algorithms for Growing Prioritized Disks and Rectangles
Abstract
Motivated by map labeling, we study the problem in which we
are given a collection of n disks in the
plane that grow at possibly different speeds. Whenever two
disks meet, the one with the higher index disappears. This
problem was introduced by Funke, Krumpe, and Storandt[IWOCA 2016].
We provide the first general subquadratic algorithm for computing
the times and the order of disappearance.
Our algorithm also works for other shapes (such as rectangles)
and in any fixed dimension.
Using quadtrees, we provide an alternative
algorithm that runs in near linear time, although
this second algorithm has a logarithmic dependence
on either the ratio of the fastest speed to the slowest speed of disks
or the spread of the disk centers
(the ratio of the maximum to the minimum distance between them).
Our result improves the running times of previous algorithms by
Funke, Krumpe, and
Storandt [IWOCA 2016], Bahrdt et al. [ALENEX 2017], and
Funke and Storandt [EWCG 2017].
Finally, we give an \Omega(n\log n) lower bound on the
problem, showing that our quadtree algorithms are almost tight.
Cite as
Hee-Kap Ahn, Sang Won Bae, Jongmin Choi, Matias Korman, Wolfgang Mulzer, Eunjin Oh, Ji-won Park, André van Renssen, and Antoine Vigneron. Faster Algorithms for Growing Prioritized Disks and Rectangles. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 3:1-3:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{ahn_et_al:LIPIcs.ISAAC.2017.3,
author = {Ahn, Hee-Kap and Bae, Sang Won and Choi, Jongmin and Korman, Matias and Mulzer, Wolfgang and Oh, Eunjin and Park, Ji-won and van Renssen, Andr\'{e} and Vigneron, Antoine},
title = {{Faster Algorithms for Growing Prioritized Disks and Rectangles}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {3:1--3:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.3},
URN = {urn:nbn:de:0030-drops-82199},
doi = {10.4230/LIPIcs.ISAAC.2017.3},
annote = {Keywords: map labeling, growing disks, elimination order}
}
Document
Placing your Coins on a Shelf
Abstract
We consider the problem of packing a family of disks 'on a shelf,'
that is, such that each disk touches the x-axis from above and such that no two disks overlap. We prove that the problem of minimizing the distance between the leftmost point and the rightmost point of any disk is NP-hard. On the positive side, we show how to approximate this problem within a factor of 4/3 in O(n log n) time, and provide an O(n log n)-time exact algorithm for a special case, in particular when the ratio between the largest and smallest radius is at most four.
Cite as
Helmut Alt, Kevin Buchin, Steven Chaplick, Otfried Cheong, Philipp Kindermann, Christian Knauer, and Fabian Stehn. Placing your Coins on a Shelf. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{alt_et_al:LIPIcs.ISAAC.2017.4,
author = {Alt, Helmut and Buchin, Kevin and Chaplick, Steven and Cheong, Otfried and Kindermann, Philipp and Knauer, Christian and Stehn, Fabian},
title = {{Placing your Coins on a Shelf}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {4:1--4:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.4},
URN = {urn:nbn:de:0030-drops-82145},
doi = {10.4230/LIPIcs.ISAAC.2017.4},
annote = {Keywords: packing problems, approximation algorithms, NP-hardness}
}
Document
On the Number of p4-Tilings by an n-Omino
Abstract
A plane tiling by the copies of a polyomino is called isohedral if every pair of copies in the tiling has a symmetry of the tiling that maps one copy to the other. We show that, for every $n$-omino (i.e., polyomino consisting of n cells),
the number of non-equivalent isohedral tilings generated by 90 degree rotations, so called p4-tilings or quarter-turn tilings, is bounded by a constant (independent of n). The proof relies on the analysis of the factorization of the boundary word of a polyomino.
Cite as
Kazuyuki Amano and Yoshinobu Haruyama. On the Number of p4-Tilings by an n-Omino. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 5:1-5:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{amano_et_al:LIPIcs.ISAAC.2017.5,
author = {Amano, Kazuyuki and Haruyama, Yoshinobu},
title = {{On the Number of p4-Tilings by an n-Omino}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {5:1--5:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.5},
URN = {urn:nbn:de:0030-drops-82498},
doi = {10.4230/LIPIcs.ISAAC.2017.5},
annote = {Keywords: polyomino, plane tiling, isohedral tiling, word factorization}
}
Document
Network Optimization on Partitioned Pairs of Points
Abstract
Given n pairs of points, S = {{p_1, q_1}, {p_2, q_2}, ..., {p_n, q_n}}, in some metric space, we study the problem of two-coloring the points within each pair, red and blue, to optimize the cost of a pair of node-disjoint networks, one over the red points and one over the blue points. In this paper we consider our network structures to be spanning trees, traveling salesman tours or matchings. We consider several different weight functions computed over the network structures induced, as well as several different objective functions. We show that some of these problems are NP-hard, and provide constant factor approximation algorithms in all cases.
Cite as
Esther M. Arkin, Aritra Banik, Paz Carmi, Gui Citovsky, Su Jia, Matthew J. Katz, Tyler Mayer, and Joseph S. B. Mitchell. Network Optimization on Partitioned Pairs of Points. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 6:1-6:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{arkin_et_al:LIPIcs.ISAAC.2017.6,
author = {Arkin, Esther M. and Banik, Aritra and Carmi, Paz and Citovsky, Gui and Jia, Su and Katz, Matthew J. and Mayer, Tyler and Mitchell, Joseph S. B.},
title = {{Network Optimization on Partitioned Pairs of Points}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {6:1--6:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.6},
URN = {urn:nbn:de:0030-drops-82700},
doi = {10.4230/LIPIcs.ISAAC.2017.6},
annote = {Keywords: Network Optimization, TSP tour, Matching, Spanning Tree, Pairs, Partition, Algorithms, Complexity}
}
Document
Voronoi Diagrams for Parallel Halflines and Line Segments in Space
Abstract
We consider the Euclidean Voronoi diagram for a set of $n$ parallel halflines in 3-space.
A relation of this diagram to planar power diagrams is shown, and is used to
analyze its geometric and topological properties. Moreover, an easy-to-implement
space sweep algorithm is proposed that computes the Voronoi diagram for parallel halflines
at logarithmic cost per face. Previously only an approximation algorithm for this problem was known.
Our method of construction generalizes to Voronoi diagrams for parallel line segments,
and to higher dimensions.
Cite as
Franz Aurenhammer, Bert Jüttler, and Günter Paulini. Voronoi Diagrams for Parallel Halflines and Line Segments in Space. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 7:1-7:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{aurenhammer_et_al:LIPIcs.ISAAC.2017.7,
author = {Aurenhammer, Franz and J\"{u}ttler, Bert and Paulini, G\"{u}nter},
title = {{Voronoi Diagrams for Parallel Halflines and Line Segments in Space}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {7:1--7:10},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.7},
URN = {urn:nbn:de:0030-drops-82157},
doi = {10.4230/LIPIcs.ISAAC.2017.7},
annote = {Keywords: Voronoi diagram, line segments, space-sweep algorithm}
}
Document
Faster Algorithms for Half-Integral T-Path Packing
Abstract
Let G = (V, E) be an undirected graph, a subset of vertices T be a set of terminals. Then a natural combinatorial problem consists in finding the maximum number of vertex-disjoint paths connecting distinct terminals. For this problem, a clever construction suggested by Gallai reduces it to computing a maximum non-bipartite matching and thus gives an O(mn^1/2 log(n^2/m)/log(n))-time algorithm (hereinafter n := |V|, m := |E|).
Now let us consider the fractional relaxation, i.e. allow T-path packings with arbitrary nonnegative real weights. It is known that there always exists a half-integral solution, that is, one only needs to assign weights 0, 1/2, 1 to maximize the total weight of T-paths. It is also known that an optimum half-integral packing can be found in strongly-polynomial time but the actual time bounds are far from being satisfactory.
In this paper we present a novel algorithm that solves the half-integral problem within O(mn^1/2 log(n^2/m)/log(n)) time, thus matching the complexities of integral and half-integral versions.
Cite as
Maxim Babenko and Stepan Artamonov. Faster Algorithms for Half-Integral T-Path Packing. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 8:1-8:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{babenko_et_al:LIPIcs.ISAAC.2017.8,
author = {Babenko, Maxim and Artamonov, Stepan},
title = {{Faster Algorithms for Half-Integral T-Path Packing}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {8:1--8:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.8},
URN = {urn:nbn:de:0030-drops-82750},
doi = {10.4230/LIPIcs.ISAAC.2017.8},
annote = {Keywords: graph algorithms, multiflows, path packings, matchings}
}
Document
Shortcuts for the Circle
Abstract
Let C be the unit circle in R^2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k >= 1 shortcuts on C such that the diameter of the resulting graph is minimized.
We analyze for each k with 1 <= k <= 7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a strictly decreasing function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2 + Theta(1/k^(2/3)) for any k.
Cite as
Sang Won Bae, Mark de Berg, Otfried Cheong, Joachim Gudmundsson, and Christos Levcopoulos. Shortcuts for the Circle. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 9:1-9:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{bae_et_al:LIPIcs.ISAAC.2017.9,
author = {Bae, Sang Won and de Berg, Mark and Cheong, Otfried and Gudmundsson, Joachim and Levcopoulos, Christos},
title = {{Shortcuts for the Circle}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {9:1--9:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.9},
URN = {urn:nbn:de:0030-drops-82133},
doi = {10.4230/LIPIcs.ISAAC.2017.9},
annote = {Keywords: Computational geometry, graph augmentation problem, circle, shortcut, diameter}
}
Document
Routing in Polygonal Domains
Abstract
We consider the problem of routing a data packet through the visibility graph of a polygonal domain P with n vertices and h holes. We may preprocess P to obtain a label and a routing table for each vertex. Then, we must be able to route a data packet between any two vertices p and q of P , where each step must use only the label of the target node q and the routing table of the current node.
For any fixed eps > 0, we pre ent a routing scheme that always achieves a routing path that exceeds the shortest path by a factor of at most 1 + eps. The labels have O(log n) bits, and the routing tables are of size O((eps^{-1} + h) log n). The preprocessing time is O(n^2 log n + hn^2 + eps^{-1}hn). It can be improved to O(n 2 + eps^{-1}n) for simple polygons.
Cite as
Bahareh Banyassady, Man-Kwun Chiu, Matias Korman, Wolfgang Mulzer, André van Renssen, Marcel Roeloffzen, Paul Seiferth, Yannik Stein, Birgit Vogtenhuber, and Max Willert. Routing in Polygonal Domains. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{banyassady_et_al:LIPIcs.ISAAC.2017.10,
author = {Banyassady, Bahareh and Chiu, Man-Kwun and Korman, Matias and Mulzer, Wolfgang and van Renssen, Andr\'{e} and Roeloffzen, Marcel and Seiferth, Paul and Stein, Yannik and Vogtenhuber, Birgit and Willert, Max},
title = {{Routing in Polygonal Domains}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {10:1--10:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.10},
URN = {urn:nbn:de:0030-drops-82379},
doi = {10.4230/LIPIcs.ISAAC.2017.10},
annote = {Keywords: polygonal domains, routing scheme, small stretch,Yao graph}
}
Document
Tilt Assembly: Algorithms for Micro-Factories that Build Objects with Uniform External Forces
Abstract
We present algorithmic results for the parallel assembly of many micro-scale objects in two and three dimensions from tiny particles, which has been proposed in the context of programmable matter and self-assembly for building high-yield micro-factories. The underlying model has particles moving under the influence of uniform external forces until they hit an obstacle; particles can bond when being forced together with another appropriate particle.
Due to the physical and geometric constraints, not all shapes can be built in this manner; this gives rise to the Tilt Assembly Problem (TAP) of deciding constructibility. For simply-connected polyominoes P in 2D consisting of N unit-squares ("tiles"), we prove that TAP can be decided in O(N log N) time. For the optimization variant MaxTAP (in which the
objective is to construct a subshape of maximum possible size), we show polyAPX-hardness: unless P=NP, MaxTAP cannot be approximated within a factor of N^(1/3); for tree-shaped structures, we give an N^(1/2)-approximation algorithm. For the efficiency of the assembly process itself, we show that any constructible shape allows pipelined assembly, which produces copies of P in O(1) amortized time, i.e., N copies of P in O(N) time steps. These considerations can be extended to three-dimensional objects: For the class of polycubes P we prove that it is NP-hard to decide whether it is possible to construct a path between two points of P; it is also NP-hard to decide constructibility of a polycube P. Moreover, it is expAPX-hard to maximize a path from a given start point.
Cite as
Aaron T. Becker, Sándor P. Fekete, Phillip Keldenich, Dominik Krupke, Christian Rieck, Christian Scheffer, and Arne Schmidt. Tilt Assembly: Algorithms for Micro-Factories that Build Objects with Uniform External Forces. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 11:1-11:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{becker_et_al:LIPIcs.ISAAC.2017.11,
author = {Becker, Aaron T. and Fekete, S\'{a}ndor P. and Keldenich, Phillip and Krupke, Dominik and Rieck, Christian and Scheffer, Christian and Schmidt, Arne},
title = {{Tilt Assembly: Algorithms for Micro-Factories that Build Objects with Uniform External Forces}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {11:1--11:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.11},
URN = {urn:nbn:de:0030-drops-82214},
doi = {10.4230/LIPIcs.ISAAC.2017.11},
annote = {Keywords: Programmable matter, micro-factories, tile assembly, tilt, approximation, hardness}
}
Document
A Simple Greedy Algorithm for Dynamic Graph Orientation
Abstract
Graph orientations with low out-degree are one of several ways to efficiently store sparse graphs. If the graphs allow for insertion and deletion of edges, one may have to flip the orientation of some edges to prevent blowing up the maximum out-degree. We use arboricity as our sparsity measure. With an immensely simple greedy algorithm, we get parametrized trade-off bounds between out-degree and worst case number of flips, which previously only existed for amortized number of flips. We match the previous best worst-case algorithm (in O(log n) flips) for general arboricity and beat it for either constant or super-logarithmic arboricity. We also match a previous best amortized result for at least logarithmic arboricity, and give the first results with worst-case O(1) and O(sqrt(log n)) flips nearly matching degree bounds to their respective amortized solutions.
Cite as
Edvin Berglin and Gerth Stølting Brodal. A Simple Greedy Algorithm for Dynamic Graph Orientation. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 12:1-12:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{berglin_et_al:LIPIcs.ISAAC.2017.12,
author = {Berglin, Edvin and St{\o}lting Brodal, Gerth},
title = {{A Simple Greedy Algorithm for Dynamic Graph Orientation}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {12:1--12:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.12},
URN = {urn:nbn:de:0030-drops-82637},
doi = {10.4230/LIPIcs.ISAAC.2017.12},
annote = {Keywords: Dynamic graph algorithms, graph arboricity, edge orientations}
}
Document
Crossing Number for Graphs with Bounded~Pathwidth
Abstract
The crossing number is the smallest number of pairwise edge crossings when drawing a graph into the plane. There are only very few graph classes for which the exact crossing number is known or for which there at least exist constant approximation ratios. Furthermore, up to now, general crossing number computations have never been successfully tackled using bounded width of graph decompositions, like treewidth or pathwidth.
In this paper, we for the first time show that crossing number is tractable (even in linear time) for maximal graphs of bounded pathwidth 3. The technique also shows that the crossing number and the rectilinear (a.k.a. straight-line) crossing number are identical for this graph class, and that we require only an O(n)xO(n)-grid to achieve such a drawing.
Our techniques can further be extended to devise a 2-approximation for general graphs with pathwidth 3, and a 4w^3-approximation for maximal graphs of pathwidth w. This is a constant approximation for bounded pathwidth graphs.
Cite as
Therese Biedl, Markus Chimani, Martin Derka, and Petra Mutzel. Crossing Number for Graphs with Bounded~Pathwidth. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 13:1-13:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{biedl_et_al:LIPIcs.ISAAC.2017.13,
author = {Biedl, Therese and Chimani, Markus and Derka, Martin and Mutzel, Petra},
title = {{Crossing Number for Graphs with Bounded\textasciitildePathwidth}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {13:1--13:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.13},
URN = {urn:nbn:de:0030-drops-82570},
doi = {10.4230/LIPIcs.ISAAC.2017.13},
annote = {Keywords: Crossing Number, Graphs with Bounded Pathwidth}
}
Document
An Improved Algorithm for Computing All the Best Swap Edges of a Tree Spanner
Abstract
A tree sigma-spanner of a positively real-weighted n-vertex and m-edge undirected graph G is a spanning tree T of G which approximately preserves (i.e., up to a multiplicative stretch factor sigma) distances in G.
Tree spanners with provably good stretch factors find applications in communication networks, distributed systems, and network design. However, finding an optimal or even a good tree spanner is a very hard computational task. Thus, if one has to face a transient edge failure in T, the overall effort that has to be afforded to rebuild a new tree spanner (i.e., computational costs, set-up of new links, updating of the routing tables, etc.) can be rather prohibitive. To circumvent this drawback, an effective alternative is that of associating with each tree edge a best possible (in terms of resulting stretch) swap edge -- a well-established approach in the literature for several other tree topologies. Correspondingly, the problem of computing all the best swap edges of a tree spanner is a challenging algorithmic problem, since solving it efficiently means to exploit the structure of shortest paths not only in G, but also in all the scenarios in which an edge of T has failed. For this problem we provide a very efficient solution, running in O(n^2 log^4 n) time, which drastically improves (almost by a quadratic factor in n in dense graphs!) on the previous known best result.
Cite as
Davide Bilò, Feliciano Colella, Luciano Gualà, Stefano Leucci, and Guido Proietti. An Improved Algorithm for Computing All the Best Swap Edges of a Tree Spanner. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 14:1-14:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{bilo_et_al:LIPIcs.ISAAC.2017.14,
author = {Bil\`{o}, Davide and Colella, Feliciano and Gual\`{a}, Luciano and Leucci, Stefano and Proietti, Guido},
title = {{An Improved Algorithm for Computing All the Best Swap Edges of a Tree Spanner}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {14:1--14:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.14},
URN = {urn:nbn:de:0030-drops-82663},
doi = {10.4230/LIPIcs.ISAAC.2017.14},
annote = {Keywords: Transient edge failure, Swap algorithm, Tree spanner}
}
Document
Decomposing a Graph into Shortest Paths with Bounded Eccentricity
Abstract
We introduce the problem of hub-laminar decomposition which generalizes that of computing a shortest path with minimum eccentricity (MESP). Intuitively, it consists in decomposing a graph into several paths that collectively have small eccentricity and meet only near their extremities. The problem is related to computing an isometric cycle with minimum eccentricity (MEIC). It is also linked to DNA reconstitution in the context of metagenomics in biology. We show that a graph having such a decomposition with long enough paths can be decomposed in polynomial time with approximated guaranties on the parameters of the decomposition. Moreover, such a decomposition with few paths allows to compute a compact representation of distances with additive distortion. We also show that having an isometric cycle with small eccentricity is related to the possibility of embedding the graph in a cycle with low distortion.
Cite as
Etienne Birmelé, Fabien de Montgolfier, Léo Planche, and Laurent Viennot. Decomposing a Graph into Shortest Paths with Bounded Eccentricity. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 15:1-15:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{birmele_et_al:LIPIcs.ISAAC.2017.15,
author = {Birmel\'{e}, Etienne and de Montgolfier, Fabien and Planche, L\'{e}o and Viennot, Laurent},
title = {{Decomposing a Graph into Shortest Paths with Bounded Eccentricity}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {15:1--15:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.15},
URN = {urn:nbn:de:0030-drops-82621},
doi = {10.4230/LIPIcs.ISAAC.2017.15},
annote = {Keywords: Graph Decomposition, Graph Clustering, Distance Labeling, BFS, MESP}
}
Document
Independent Feedback Vertex Set for P_5-free Graphs
Abstract
The NP-complete problem Feedback Vertex Set is to decide if it is possible, for a given integer k>=0, to delete at most k vertices from a given graph so that what remains is a forest. The variant in which the deleted vertices must form an independent set is called Independent Feedback Vertex Set and is also NP-complete. In fact, even deciding if an independent feedback vertex set exists is NP-complete and this problem is closely related to the 3-Colouring problem, or equivalently, to the problem of deciding if a graph has an independent odd cycle transversal, that is, an independent set of vertices whose deletion makes the graph bipartite. We initiate a systematic study of the complexity of Independent Feedback Vertex Set for H-free graphs. We prove that it is NP-complete if H contains a claw or cycle. Tamura, Ito and Zhou proved that it is polynomial-time solvable for P_4-free graphs. We show that it remains in P for P_5-free graphs. We prove analogous results for the Independent Odd Cycle Transversal problem, which asks if a graph has an independent odd cycle transversal of size at most k for a given integer k>=0.
Cite as
Marthe Bonamy, Konrad K. Dabrowski, Carl Feghali, Matthew Johnson, and Daniël Paulusma. Independent Feedback Vertex Set for P_5-free Graphs. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 16:1-16:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{bonamy_et_al:LIPIcs.ISAAC.2017.16,
author = {Bonamy, Marthe and Dabrowski, Konrad K. and Feghali, Carl and Johnson, Matthew and Paulusma, Dani\"{e}l},
title = {{Independent Feedback Vertex Set for P\underline5-free Graphs}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {16:1--16:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.16},
URN = {urn:nbn:de:0030-drops-82308},
doi = {10.4230/LIPIcs.ISAAC.2017.16},
annote = {Keywords: feedback vertex set, odd cycle transversal, independent set, H-free graph}
}
Document
On the Convergence Time of a Natural Dynamics for Linear Programming
Abstract
We consider a system of nonlinear ordinary differential equations for the solution of linear programming (LP) problems that was first proposed in the mathematical biology literature as a model for the foraging behavior of acellular slime mold Physarum polycephalum, and more recently considered as a method to solve LP instances. We study the convergence time of the continuous Physarum dynamics in the context of the linear programming problem, and derive a new time bound to approximate optimality that depends on the relative entropy between projected versions of the optimal point and of the initial point. The bound scales logarithmically with the LP cost coefficients and linearly with the inverse of the relative accuracy, establishing the efficiency of the dynamics for arbitrary LP instances with positive costs.
Cite as
Vincenzo Bonifaci. On the Convergence Time of a Natural Dynamics for Linear Programming. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 17:1-17:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{bonifaci:LIPIcs.ISAAC.2017.17,
author = {Bonifaci, Vincenzo},
title = {{On the Convergence Time of a Natural Dynamics for Linear Programming}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {17:1--17:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.17},
URN = {urn:nbn:de:0030-drops-82274},
doi = {10.4230/LIPIcs.ISAAC.2017.17},
annote = {Keywords: linear programming, natural algorithm, Physarum polycephalum, relative entropy, Mirror Descent}
}
Document
Routing on the Visibility Graph
Abstract
We consider the problem of routing on a network in the presence of line segment constraints (i.e., obstacles that edges in our network are not allowed to cross). Let P be a set of n vertices in the plane and let S be a set of line segments between the vertices in P, with no two line segments intersecting properly. We present two 1-local O(1)-memory routing algorithms on the visibility graph of P with respect to a set of constraints S (i.e., the algorithms never look beyond the direct neighbours of the current location and store only a constant amount of information). Contrary to all existing routing algorithms, our routing algorithms do not require us to compute a plane subgraph of the visibility graph in order to route on it.
Cite as
Prosenjit Bose, Matias Korman, André van Renssen, and Sander Verdonschot. Routing on the Visibility Graph. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 18:1-18:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{bose_et_al:LIPIcs.ISAAC.2017.18,
author = {Bose, Prosenjit and Korman, Matias and van Renssen, Andr\'{e} and Verdonschot, Sander},
title = {{Routing on the Visibility Graph}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {18:1--18:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.18},
URN = {urn:nbn:de:0030-drops-82224},
doi = {10.4230/LIPIcs.ISAAC.2017.18},
annote = {Keywords: Routing, constraints, visibility graph, Theta-graph}
}
Document
An FPTAS of Minimizing Total Weighted Completion Time on Single Machine with Position Constraint
Abstract
In this paper we study the classical scheduling problem of minimizing the total weighted completion time on a single machine with the constraint that one specific job must be scheduled at a specified position. We give dynamic programs with pseudo-polynomial running time, and a fully polynomial-time approximation scheme (FPTAS).
Cite as
Gruia Calinescu, Florian Jaehn, Minming Li, and Kai Wang. An FPTAS of Minimizing Total Weighted Completion Time on Single Machine with Position Constraint. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 19:1-19:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{calinescu_et_al:LIPIcs.ISAAC.2017.19,
author = {Calinescu, Gruia and Jaehn, Florian and Li, Minming and Wang, Kai},
title = {{An FPTAS of Minimizing Total Weighted Completion Time on Single Machine with Position Constraint}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {19:1--19:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.19},
URN = {urn:nbn:de:0030-drops-82335},
doi = {10.4230/LIPIcs.ISAAC.2017.19},
annote = {Keywords: FPTAS, Scheduling, Approximation Algorithm}
}
Document
An Efficient Fixed-Parameter Algorithm for the 2-Plex Bipartition Problem
Abstract
Given a graph G=(V, E), an s-plex S\subseteq V is a vertex subset such that for v\in S the degree of v in G[S] is at least |S|-s. An s-plex bipartition \mathcal{P}=(V_1, V_2) is a bipartition of G=(V, E), V=V_1\uplus V_2, satisfying that both V_1 and V_2 are s-plexes. Given an instance G=(V, E) and a parameter k, the s-Plex Bipartition problem asks whether there exists an s-plex bipartition of G such that min{|V_1|, |V_2|\}\leq k. The s-Plex Bipartition problem is NP-complete. However, it is still open whether this problem is fixed-parameter tractable. In this paper, we give a fixed-parameter algorithm for 2-Plex Bipartition running in time O*(2.4143^k). A graph G = (V, E) is called defective (p, d)-colorable if it admits a vertex coloring with p colors such that each color class in G induces a subgraph of maximum degree at most d. A graph G admits an s-plex bipartition if and only if the complement graph of G, \bar{G}, admits a defective (2, s-1)-coloring such that one of the two color classes is of size at most k. By applying our fixed-parameter algorithm as a subroutine, one can find a defective (2,1)-coloring with one of the two colors of minimum cardinality for a given graph in O*(1.5539^n) time where n is the number of vertices in the input graph.
Cite as
Li-Hsuan Chen, Sun-Yuan Hsieh, Ling-Ju Hung, and Peter Rossmanith. An Efficient Fixed-Parameter Algorithm for the 2-Plex Bipartition Problem. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 20:1-20:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{chen_et_al:LIPIcs.ISAAC.2017.20,
author = {Chen, Li-Hsuan and Hsieh, Sun-Yuan and Hung, Ling-Ju and Rossmanith, Peter},
title = {{An Efficient Fixed-Parameter Algorithm for the 2-Plex Bipartition Problem}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {20:1--20:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.20},
URN = {urn:nbn:de:0030-drops-82458},
doi = {10.4230/LIPIcs.ISAAC.2017.20},
annote = {Keywords: 2-plex, 2-plex bipartition, bounded-degree-1 set bipartition, defective (2,1)-coloring}
}
Document
Smart Contract Execution - the (+-)-Biased Ballot Problem
Abstract
Transaction system build on top of blockchain, especially smart contract, is becoming an important part of world economy. However, there is a lack of formal study on the behavior of users in these systems, which leaves the correctness and security of such system without a solid foundation. Unlike mining, in which the reward for mining a block is fixed, different execution results of a smart contract may lead to significantly different payoffs of users, which gives more incentives for some user to follow a branch that contains a wrong result, even if the branch is shorter. It is thus important to understand the exact probability that a branch is being selected by the system. We formulate this problem as the (+-)-Biased Ballot Problem as follows: there are n voters one by one voting for either of the two candidates A and B. The probability of a user voting for A or B depends on whether the difference between the current votes of A and B is positive or negative. Our model takes into account the behavior of three different kinds of users when a branch occurs in the system -- users having preference over a certain branch based on the history of their transactions, and users being indifferent and simply follow the longest chain. We study two important probabilities that are closely related with a blockchain based system - the probability that A wins at last, and the probability that A receives d votes first. We show how to recursively calculate the two probabilities for any fixed n and d, and also discuss their asymptotic values when n and d are sufficiently large.
Cite as
Lin Chen, Lei Xu, Zhimin Gao, Nolan Shah, Yang Lu, and Weidong Shi. Smart Contract Execution - the (+-)-Biased Ballot Problem. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 21:1-21:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{chen_et_al:LIPIcs.ISAAC.2017.21,
author = {Chen, Lin and Xu, Lei and Gao, Zhimin and Shah, Nolan and Lu, Yang and Shi, Weidong},
title = {{Smart Contract Execution - the (+-)-Biased Ballot Problem}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {21:1--21:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.21},
URN = {urn:nbn:de:0030-drops-82388},
doi = {10.4230/LIPIcs.ISAAC.2017.21},
annote = {Keywords: Blockchain, Probability, Random Walk, Smart Contract}
}
Document
Study of a Combinatorial Game in Graphs Through Linear Programming
Abstract
In the Spy Game played on a graph G, a single spy travels the ertices of G at speed s, while multiple slow guards strive to have, at all times, one of them within distance d of that spy. In order to determine the smallest number of guards necessary for this task, we analyze the game through a Linear Programming formulation and the fractional strategies it yields for the guards. We then show the equivalence of fractional and integral strategies in trees. This allows us to design a polynomial-time algorithm for computing an optimal strategy in this class of graphs. Using duality in Linear Programming, we also provide non-trivial bounds on the fractional guardnumber of grids and torus. We believe that the approach using fractional relaxation and Linear Programming is promising to obtain new results in the field of combinatorial games.
Cite as
Nathann Cohen, Fionn Mc Inerney, Nicolas Nisse, and Stéphane Pérennes. Study of a Combinatorial Game in Graphs Through Linear Programming. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 22:1-22:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{cohen_et_al:LIPIcs.ISAAC.2017.22,
author = {Cohen, Nathann and Mc Inerney, Fionn and Nisse, Nicolas and P\'{e}rennes, St\'{e}phane},
title = {{Study of a Combinatorial Game in Graphs Through Linear Programming}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {22:1--22:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.22},
URN = {urn:nbn:de:0030-drops-82254},
doi = {10.4230/LIPIcs.ISAAC.2017.22},
annote = {Keywords: Turn-by-turn games in graphs, Graph algorithms, Linear Programming}
}
Document
On Maximal Cliques with Connectivity Constraints in Directed Graphs
Abstract
Finding communities in the form of cohesive subgraphs is a fundamental problem in network analysis. In domains that model networks as undirected graphs, communities are generally associated with dense subgraphs, and many community models have been proposed.
Maximal cliques are arguably the most widely studied among such models, with early works dating back to the '60s, and a continuous stream of research up to the present. In domains that model networks as directed graphs, several approaches for community detection have been proposed, but there seems to be no clear model of cohesive subgraph, i.e., of what a community should look like. We extend the fundamental model of clique to directed graphs, adding the natural constraint of strong connectivity within the clique. We characterize the problem by giving a tight bound for the number of such cliques in a graph, and highlighting useful structural properties. We then exploit these properties to produce the first algorithm with polynomial delay for enumerating maximal strongly connected cliques.
Cite as
Alessio Conte, Mamadou Moustapha Kanté, Takeaki Uno, and Kunihiro Wasa. On Maximal Cliques with Connectivity Constraints in Directed Graphs. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 23:1-23:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{conte_et_al:LIPIcs.ISAAC.2017.23,
author = {Conte, Alessio and Kant\'{e}, Mamadou Moustapha and Uno, Takeaki and Wasa, Kunihiro},
title = {{On Maximal Cliques with Connectivity Constraints in Directed Graphs}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {23:1--23:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.23},
URN = {urn:nbn:de:0030-drops-82284},
doi = {10.4230/LIPIcs.ISAAC.2017.23},
annote = {Keywords: Enumeration algorithms, Bounded delay, Directed graphs, Community structure, Network analytics}
}
Document
Square-Contact Representations of Partial 2-Trees and Triconnected Simply-Nested Graphs
Abstract
A square-contact representation of a planar graph G = (V,E) maps vertices in V to interior-disjoint axis-aligned squares in the plane and edges in E to adjacencies between the sides of the corresponding squares. In this paper, we study proper square-contact representations of planar graphs, in which any two squares are either disjoint or share infinitely many points.
We characterize the partial 2-trees and the triconnected cycle-trees allowing for such representations. For partial 2-trees our characterization uses a simple forbidden subgraph whose structure forces a separating triangle in any embedding. For the triconnected cycle-trees, a subclass of the triconnected simply-nested graphs, we use a new structural decomposition for the graphs in this family, which may be of independent interest. Finally, we study square-contact representations of general triconnected simply-nested graphs with respect to their outerplanarity index.
Cite as
Giordano Da Lozzo, William E. Devanny, David Eppstein, and Timothy Johnson. Square-Contact Representations of Partial 2-Trees and Triconnected Simply-Nested Graphs. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 24:1-24:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{dalozzo_et_al:LIPIcs.ISAAC.2017.24,
author = {Da Lozzo, Giordano and Devanny, William E. and Eppstein, David and Johnson, Timothy},
title = {{Square-Contact Representations of Partial 2-Trees and Triconnected Simply-Nested Graphs}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {24:1--24:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.24},
URN = {urn:nbn:de:0030-drops-82675},
doi = {10.4230/LIPIcs.ISAAC.2017.24},
annote = {Keywords: Square-Contact Representations, Partial 2-Trees, Simply-Nested Graphs}
}
Document
Faster DBScan and HDBScan in Low-Dimensional Euclidean Spaces
Abstract
We present a new algorithm for the widely used density-based clustering method DBScan. Our algorithm computes the DBScan-clustering in O(n log n) time in R^2, irrespective of the scale parameter \eps, but assuming the second parameter MinPts is set to a fixed constant, as is the case in practice.
We also present an O(n log n) randomized algorithm for HDBScan in the plane---HDBScans is a hierarchical version of DBScan introduced recently---and we show how to compute an approximate version of HDBScan in near-linear time in any fixed dimension.
Cite as
Mark de Berg, Ade Gunawan, and Marcel Roeloffzen. Faster DBScan and HDBScan in Low-Dimensional Euclidean Spaces. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 25:1-25:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{deberg_et_al:LIPIcs.ISAAC.2017.25,
author = {de Berg, Mark and Gunawan, Ade and Roeloffzen, Marcel},
title = {{Faster DBScan and HDBScan in Low-Dimensional Euclidean Spaces}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {25:1--25:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.25},
URN = {urn:nbn:de:0030-drops-82102},
doi = {10.4230/LIPIcs.ISAAC.2017.25},
annote = {Keywords: Density-based clustering, hierarchical clustering}
}
Document
Fully-Dynamic and Kinetic Conflict-Free Coloring of Intervals with Respect to Points
Abstract
We introduce the fully-dynamic conflict-free coloring problem for a set S of intervals in R^1 with respect to points, where the goal is to maintain a conflict-free coloring for S under insertions and deletions. A coloring is conflict-free if for each point p contained in some interval, p is contained in an interval whose color is not shared with any other interval containing p. We investigate trade-offs between the number of colors used and the number of intervals that are recolored upon insertion or deletion of an interval. Our results include:
- a lower bound on the number of recolorings as a function of the number of colors, which implies that with O(1) recolorings per update the worst-case number of colors is Omega(log n/log log n), and that any strategy using O(1/epsilon) colors needs Omega(epsilon n^epsilon) recolorings;
- a coloring strategy that uses O(log n) colors at the cost of O(log n) recolorings, and another strategy that uses O(1/epsilon) colors at the cost of O(n^epsilon/epsilon) recolorings;
- stronger upper and lower bounds for special cases.
We also consider the kinetic setting where the intervals move continuously (but there are no insertions or deletions); here we show how to maintain a coloring with only four colors at the cost of three recolorings per event and show this is tight.
Cite as
Mark de Berg, Tim Leijsen, Aleksandar Markovic, André van Renssen, Marcel Roeloffzen, and Gerhard Woeginger. Fully-Dynamic and Kinetic Conflict-Free Coloring of Intervals with Respect to Points. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 26:1-26:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{deberg_et_al:LIPIcs.ISAAC.2017.26,
author = {de Berg, Mark and Leijsen, Tim and Markovic, Aleksandar and van Renssen, Andr\'{e} and Roeloffzen, Marcel and Woeginger, Gerhard},
title = {{Fully-Dynamic and Kinetic Conflict-Free Coloring of Intervals with Respect to Points}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {26:1--26:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.26},
URN = {urn:nbn:de:0030-drops-82683},
doi = {10.4230/LIPIcs.ISAAC.2017.26},
annote = {Keywords: Conflict-free colorings, Dynamic data structures, Kinetic data structures}
}
Document
Dynamic Conflict-Free Colorings in the Plane
Abstract
We study dynamic conflict-free colorings in the plane, where the goal is to maintain a conflict-free coloring (CF-coloring for short) under insertions and deletions.
- First we consider CF-colorings of a set S of unit squares with respect to points. Our method maintains a CF-coloring that uses O(log n) colors at any time, where n is the current number of squares in S, at the cost of only O(log n) recolorings per insertion or deletion We generalize the method to rectangles whose sides have lengths in the range [1, c], where c is a fixed constant. Here the number of used colors becomes O(log^2 n). The method also extends to arbitrary rectangles whose coordinates come from a fixed universe of size N, yielding O(log^2 N log^2 n) colors. The number of recolorings for both methods stays in O(log n).
- We then present a general framework to maintain a CF-coloring under insertions for sets of objects that admit a unimax coloring with a small number of colors in the static case. As an application we show how to maintain a CF-coloring with O(log^3 n) colors for disks (or other objects with linear union complexity) with respect to points at the cost of O(log n) recolorings per insertion. We extend the framework to the fully-dynamic case when the static unimax coloring admits weak deletions. As an application we show how to maintain a CF-coloring with O(sqrt(n) log^2 n) colors for points with respect to rectangles, at the cost of O(log n) recolorings per insertion and O(1) recolorings per deletion.
These are the first results on fully-dynamic CF-colorings in the plane, and the first results for semi-dynamic CF-colorings for non-congruent objects.
Cite as
Mark de Berg and Aleksandar Markovic. Dynamic Conflict-Free Colorings in the Plane. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 27:1-27:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{deberg_et_al:LIPIcs.ISAAC.2017.27,
author = {de Berg, Mark and Markovic, Aleksandar},
title = {{Dynamic Conflict-Free Colorings in the Plane}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {27:1--27:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.27},
URN = {urn:nbn:de:0030-drops-82504},
doi = {10.4230/LIPIcs.ISAAC.2017.27},
annote = {Keywords: Conflict-free colorings, Dynamic data structures}
}
Document
Temporal Hierarchical Clustering
Abstract
We study hierarchical clusterings of metric spaces that change over time. This is a natural geo- metric primitive for the analysis of dynamic data sets. Specifically, we introduce and study the problem of finding a temporally coherent sequence of hierarchical clusterings from a sequence of unlabeled point sets. We encode the clustering objective by embedding each point set into an ultrametric space, which naturally induces a hierarchical clustering of the set of points. We enforce temporal coherence among the embeddings by finding correspondences between successive pairs of ultrametric spaces which exhibit small distortion in the Gromov-Hausdorff sense. We present both upper and lower bounds on the approximability of the resulting optimization problems.
Cite as
Tamal K. Dey, Alfred Rossi, and Anastasios Sidiropoulos. Temporal Hierarchical Clustering. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 28:1-28:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{dey_et_al:LIPIcs.ISAAC.2017.28,
author = {Dey, Tamal K. and Rossi, Alfred and Sidiropoulos, Anastasios},
title = {{Temporal Hierarchical Clustering}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {28:1--28:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.28},
URN = {urn:nbn:de:0030-drops-82519},
doi = {10.4230/LIPIcs.ISAAC.2017.28},
annote = {Keywords: clustering, hierarchical clustering, multi-objective optimization, dynamic metric spaces, moving point sets, approximation algorithms}
}
Document
Agnostically Learning Boolean Functions with Finite Polynomial Representation
Abstract
Agnostic learning is an extremely hard task in computational learning theory. In this paper we revisit the results in [Kalai et al. SIAM J. Comput. 2008] on agnostically learning boolean functions with finite polynomial representation and those that can be approximated by the former. An example of the former is the class of all boolean low-degree polynomials. For the former, [Kalai et al. SIAM J. Comput. 2008] introduces the l_1-polynomial regression method to learn them to error opt+epsilon. We present a simple instantiation for one step in the method and accordingly give the analysis. Moreover, we show that even ignoring this step can bring a learning result of error 2opt+epsilon as well. Then we consider applying the result for learning concept classes that can be approximated by the former to learn richer specific classes. Our result is that the class of s-term DNF formulae can be agnostically learned to error opt+epsilon with respect to arbitrary distributions for any epsilon in time poly(n^d, 1/epsilon), where d=O(\sqrt{n}\cdot s\cdot \log s\log^2(1/epsilon)).
Cite as
Ning Ding. Agnostically Learning Boolean Functions with Finite Polynomial Representation. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 29:1-29:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{ding:LIPIcs.ISAAC.2017.29,
author = {Ding, Ning},
title = {{Agnostically Learning Boolean Functions with Finite Polynomial Representation}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {29:1--29:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.29},
URN = {urn:nbn:de:0030-drops-82726},
doi = {10.4230/LIPIcs.ISAAC.2017.29},
annote = {Keywords: Agnostic Learning, Boolean Functions, Low-Degree Polynomials}
}
Document
Succinct Color Searching in One Dimension
Abstract
In this paper we study succinct data structures for one-dimensional color reporting and color counting problems.
We are given a set of n points with integer coordinates in the range [1,m] and every point is assigned a color from the set {1,...\sigma}.
A color reporting query asks for the list of distinct colors that occur in a query interval [a,b] and a color counting query asks for the number of distinct colors in [a,b].
We describe a succinct data structure that answers approximate color counting queries in O(1) time and uses \mathcal{B}(n,m) + O(n) + o(\mathcal{B}(n,m)) bits,
where \mathcal{B}(n,m) is the minimum number of bits required to represent an arbitrary set of size n from a universe of m elements. Thus we show, somewhat counterintuitively,
that it is not necessary to store colors of points in order to answer approximate color counting queries.
In the special case when points are in the rank space (i.e., when n=m), our data structure needs only O(n) bits.
Also, we show that \Omega(n) bits are necessary in that case.
Then we turn to succinct data structures for color reporting.
We describe a data structure that uses \mathcal{B}(n,m) + nH_d(S) + o(\mathcal{B}(n,m)) + o(n\lg\sigma) bits and answers queries in O(k+1) time,
where k is the number of colors in the answer, and nH_d(S) (d=\log_\sigma n) is the d-th order empirical entropy of the color sequence. Finally, we consider succinct color reporting under restricted updates. Our dynamic data structure uses nH_d(S)+o(n\lg\sigma) bits and supports queries in O(k+1) time.
Cite as
Hicham El-Zein, J. Ian Munro, and Yakov Nekrich. Succinct Color Searching in One Dimension. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 30:1-30:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{elzein_et_al:LIPIcs.ISAAC.2017.30,
author = {El-Zein, Hicham and Munro, J. Ian and Nekrich, Yakov},
title = {{Succinct Color Searching in One Dimension}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {30:1--30:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.30},
URN = {urn:nbn:de:0030-drops-82096},
doi = {10.4230/LIPIcs.ISAAC.2017.30},
annote = {Keywords: Succinct Data Structures, Range Searching, Computational Geometry}
}
Document
Conflict-Free Coloring of Intersection Graphs
Abstract
A conflict-free k-coloring of a graph G=(V,E) assigns one of k different colors to some of the vertices such that,
for every vertex v, there is a color that is assigned to exactly one vertex among v and v's neighbors.
Such colorings have applications in wireless networking, robotics, and geometry, and are well studied in graph theory.
Here we study the conflict-free coloring of geometric intersection graphs.
We demonstrate that the intersection graph of n geometric objects without fatness properties and size restrictions may have conflict-free chromatic number in \Omega(log n/log log n) and in \Omega(\sqrt{\log n}) for disks or squares of different sizes;
it is known for general graphs that the worst case is in \Theta(log^2 n).
For unit-disk intersection graphs, we prove that it is NP-complete
to decide the existence of a conflict-free coloring
with one color; we also show that six colors always suffice,
using an algorithm that colors unit disk graphs of restricted height with two colors.
We conjecture that four colors are sufficient, which we prove for unit squares instead of unit disks.
For interval graphs, we establish a tight worst-case bound of two.
Cite as
Sándor P. Fekete and Phillip Keldenich. Conflict-Free Coloring of Intersection Graphs. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 31:1-31:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{fekete_et_al:LIPIcs.ISAAC.2017.31,
author = {Fekete, S\'{a}ndor P. and Keldenich, Phillip},
title = {{Conflict-Free Coloring of Intersection Graphs}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {31:1--31:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.31},
URN = {urn:nbn:de:0030-drops-82162},
doi = {10.4230/LIPIcs.ISAAC.2017.31},
annote = {Keywords: conflict-free coloring, intersection graphs, unit disk graphs, complexity, worst-case bounds}
}
Document
On Using Toeplitz and Circulant Matrices for Johnson-Lindenstrauss Transforms
Abstract
The Johnson-Lindenstrauss lemma is one of the corner stone results in dimensionality reduction. It says that given N, for any set of N,
vectors X \subset R^n, there exists a mapping f : X --> R^m such that f(X) preserves all pairwise distances between vectors in X to within(1 ± \eps) if m = O(\eps^{-2} lg N). Much effort has gone into developing
fast embedding algorithms, with the Fast Johnson-Lindenstrauss
transform of Ailon and Chazelle being one of the most well-known
techniques. The current fastest algorithm that yields the optimal m =
O(\eps{-2}lg N) dimensions has an embedding time of O(n lg n + \eps^{-2} lg^3 N). An exciting approach towards improving this, due to Hinrichs and Vybíral, is to use a random m times n Toeplitz matrix for the
embedding. Using Fast Fourier Transform, the embedding of a vector can
then be computed in O(n lg m) time. The big question is of course
whether m = O(\eps^{-2} lg N) dimensions suffice for this technique. If
so, this would end a decades long quest to obtain faster and faster
Johnson-Lindenstrauss transforms. The current best analysis of the
embedding of Hinrichs and Vybíral shows that m = O(\eps^{-2} lg^2 N)
dimensions suffice. The main result of this paper, is a proof that
this analysis unfortunately cannot be tightened any further, i.e.,
there exists a set of N vectors requiring m = \Omega(\eps^{-2} lg^2 N)
for the Toeplitz approach to work.
Cite as
Casper Benjamin Freksen and Kasper Green Larsen. On Using Toeplitz and Circulant Matrices for Johnson-Lindenstrauss Transforms. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 32:1-32:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{freksen_et_al:LIPIcs.ISAAC.2017.32,
author = {Freksen, Casper Benjamin and Larsen, Kasper Green},
title = {{On Using Toeplitz and Circulant Matrices for Johnson-Lindenstrauss Transforms}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {32:1--32:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.32},
URN = {urn:nbn:de:0030-drops-82540},
doi = {10.4230/LIPIcs.ISAAC.2017.32},
annote = {Keywords: dimensionality reduction, Johnson-Lindenstrauss, Toeplitz matrices}
}
Document
Almost Linear Time Computation of Maximal Repetitions in Run Length Encoded Strings
Abstract
We consider the problem of computing all maximal repetitions contained in a string that is given in run-length encoding.
Given a run-length encoding of a string, we show that the maximum number of maximal repetitions contained in the string is at most m+k-1, where m is the size of the run-length encoding, and k is the number of run-length factors whose exponent is at least 2.
We also show an algorithm for computing all maximal repetitions in O(m \alpha(m)) time and O(m) space, where \alpha denotes the inverse Ackermann function.
Cite as
Yuta Fujishige, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Almost Linear Time Computation of Maximal Repetitions in Run Length Encoded Strings. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 33:1-33:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{fujishige_et_al:LIPIcs.ISAAC.2017.33,
author = {Fujishige, Yuta and Nakashima, Yuto and Inenaga, Shunsuke and Bannai, Hideo and Takeda, Masayuki},
title = {{Almost Linear Time Computation of Maximal Repetitions in Run Length Encoded Strings}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {33:1--33:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.33},
URN = {urn:nbn:de:0030-drops-82610},
doi = {10.4230/LIPIcs.ISAAC.2017.33},
annote = {Keywords: maximal repetitions,run length encoding}
}
Document
Embedding Graphs into Embedded Graphs
Abstract
A (possibly degenerate) drawing of a graph G in the plane is approximable by an embedding if it can be turned into an embedding by an arbitrarily small perturbation.
We show that testing, whether a drawing of a planar graph G in the plane is approximable by an embedding, can be carried out in polynomial time, if a desired embedding of G belongs to a fixed isotopy class, i.e., the rotation system (or equivalently the faces) of the embedding of G and the choice of outer face are fixed.
In other words, we show that c-planarity with embedded pipes is tractable for graphs with fixed embeddings.
To the best of our knowledge an analogous result was previously known essentially only when G is a cycle.
Cite as
Radoslav Fulek. Embedding Graphs into Embedded Graphs. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 34:1-34:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{fulek:LIPIcs.ISAAC.2017.34,
author = {Fulek, Radoslav},
title = {{Embedding Graphs into Embedded Graphs}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {34:1--34:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.34},
URN = {urn:nbn:de:0030-drops-82234},
doi = {10.4230/LIPIcs.ISAAC.2017.34},
annote = {Keywords: Graph embedding, C-planarity, Weakly simple polygons}
}
Document
Structural Pattern Matching - Succinctly
Abstract
Let T be a text of length n containing characters from an alphabet \Sigma, which is the union of two disjoint sets: \Sigma_s containing static characters (s-characters) and \Sigma_p containing parameterized characters (p-characters).
Each character in \Sigma_p has an associated complementary character from \Sigma_p.
A pattern P (also over \Sigma) matches an equal-length substring $S$ of T iff the s-characters match exactly, there exists a one-to-one function that renames the p-characters in S to the p-characters in P, and if a p-character x is renamed to another p-character y then the complement of x is renamed to the complement of y.
The task is to find the starting positions (occurrences) of all such substrings S.
Previous indexing solution [Shibuya, SWAT 2000], known as Structural Suffix Tree, requires \Theta(n\log n) bits of space, and can find all occ occurrences in time O(|P|\log \sigma+ occ), where \sigma = |\Sigma|.
In this paper, we present the first succinct index for this problem, which occupies n \log \sigma + O(n) bits and offers O(|P|\log\sigma+ occ\cdot \log n \log\sigma) query time.
Cite as
Arnab Ganguly, Rahul Shah, and Sharma V. Thankachan. Structural Pattern Matching - Succinctly. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 35:1-35:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{ganguly_et_al:LIPIcs.ISAAC.2017.35,
author = {Ganguly, Arnab and Shah, Rahul and Thankachan, Sharma V.},
title = {{Structural Pattern Matching - Succinctly}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {35:1--35:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.35},
URN = {urn:nbn:de:0030-drops-82566},
doi = {10.4230/LIPIcs.ISAAC.2017.35},
annote = {Keywords: Parameterized Pattern Matching, Suffix tree, Burrows-Wheeler Transform, Wavelet Tree, Fully-functional succinct tree}
}
Document
On Structural Parameterizations of the Edge Disjoint Paths Problem
Abstract
In this paper we revisit the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting every terminal pair in P. Our focus lies on structural parameterizations for the problem that allow for efficient (polynomial-time or fpt) algorithms. As our first result, we answer an open question stated in Fleszar, Mnich, and Spoerhase (2016), by showing that the problem can be solved in polynomial time if the input graph has a feedback vertex set of size one. We also show that EDP parameterized by the treewidth and the maximum degree of the input graph is fixed-parameter tractable.
Having developed two novel algorithms for EDP using structural restrictions on the input graph, we then turn our attention towards the augmented graph, i.e., the graph obtained from the input graph after adding one edge between every terminal pair. In constrast to the input graph, where EDP is known to remain NP-hard even for treewidth two, a result by Zhou et al. (2000) shows that EDP can be solved in non-uniform polynomial time if the augmented graph has constant treewidth; we note that the possible improvement of this result to an fpt-algorithm has remained open since then. We show that this is highly unlikely by establishing the W[1]-hardness of the problem parameterized by the treewidth (and even feedback vertex set) of the augmented graph. Finally, we develop an fpt-algorithm for EDP by exploiting a novel structural parameter of the augmented graph.
Cite as
Robert Ganian, Sebastian Ordyniak, and Ramanujan Sridharan. On Structural Parameterizations of the Edge Disjoint Paths Problem. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 36:1-36:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{ganian_et_al:LIPIcs.ISAAC.2017.36,
author = {Ganian, Robert and Ordyniak, Sebastian and Sridharan, Ramanujan},
title = {{On Structural Parameterizations of the Edge Disjoint Paths Problem}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {36:1--36:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.36},
URN = {urn:nbn:de:0030-drops-82555},
doi = {10.4230/LIPIcs.ISAAC.2017.36},
annote = {Keywords: edge disjoint path problem, feedback vertex set, treewidth, fracture number, parameterized complexity}
}
Document
Barrier Coverage with Non-uniform Lengths to Minimize Aggregate Movements
Abstract
Given a line segment I=[0,L], the so-called barrier, and a set of n sensors with varying ranges positioned on the line containing I, the barrier coverage problem is to move the sensors so that they cover I, while minimising the total movement. In the case when all the sensors have the same radius the problem can be solved in O(n log n) time (Andrews and Wang, Algorithmica 2017). If the sensors have different radii the problem is known to be NP-hard to approximate within a constant factor (Czyzowicz et al., ADHOC-NOW 2009).
We strengthen this result and prove that no polynomial time \rho^{1-\epsilon}-approximation algorithm exists unless P=NP, where \rho is the ratio between the largest radius and the smallest radius. Even when we restrict the number of sensors that are allowed to move by a parameter k, the problem turns out to be W[1]-hard. On the positive side we show that a ((2+\epsilon)\rho+2/\epsilon)-approximation can be computed in O(n^3/\epsilon^2) time and we prove fixed-parameter tractability when parameterized by the total movement assuming all numbers in the input are integers.
Cite as
Serge Gaspers, Joachim Gudmundsson, Julián Mestre, and Stefan Rümmele. Barrier Coverage with Non-uniform Lengths to Minimize Aggregate Movements. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 37:1-37:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{gaspers_et_al:LIPIcs.ISAAC.2017.37,
author = {Gaspers, Serge and Gudmundsson, Joachim and Mestre, Juli\'{a}n and R\"{u}mmele, Stefan},
title = {{Barrier Coverage with Non-uniform Lengths to Minimize Aggregate Movements}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {37:1--37:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.37},
URN = {urn:nbn:de:0030-drops-82591},
doi = {10.4230/LIPIcs.ISAAC.2017.37},
annote = {Keywords: Barrier coverage, Sensor movement, Approximation, Parameterized complexity}
}
Document
Sorting with Recurrent Comparison Errors
Abstract
We present a sorting algorithm for the case of recurrent random comparison errors. The algorithm essentially achieves simultaneously good properties of previous algorithms for sorting n distinct elements in this model. In particular, it runs in O(n^2) time, the maximum dislocation of the elements in the output is O(log n), while the total dislocation is O(n). These guarantees are the best possible since we prove that even randomized algorithms cannot achieve o(log n) maximum dislocation with high probability, or o(n) total dislocation in expectation, regardless of their
running time.
Cite as
Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, and Paolo Penna. Sorting with Recurrent Comparison Errors. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 38:1-38:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{geissmann_et_al:LIPIcs.ISAAC.2017.38,
author = {Geissmann, Barbara and Leucci, Stefano and Liu, Chih-Hung and Penna, Paolo},
title = {{Sorting with Recurrent Comparison Errors}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {38:1--38:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.38},
URN = {urn:nbn:de:0030-drops-82652},
doi = {10.4230/LIPIcs.ISAAC.2017.38},
annote = {Keywords: sorting, recurrent comparison error, maximum and total dislocation}
}
Document
Dominance Product and High-Dimensional Closest Pair under L_infty
Abstract
Given a set $S$ of $n$ points in \mathbb{R}^d, the Closest Pair problem is to find a pair of distinct points in S at minimum distance.
When d is constant, there are efficient algorithms that solve this problem, and fast approximate solutions for general d.
However, obtaining an exact solution in very high dimensions seems to be much less understood.
We consider the high-dimensional L_\infty Closest Pair problem, where d=n^r for some r > 0, and the underlying metric is L_\infty.
We improve and simplify previous results for L_\infty Closest Pair, showing that it can be solved by a deterministic strongly-polynomial algorithm that runs in O(DP(n,d)\log n) time, and by a randomized algorithm that runs in O(DP(n,d)) expected time, where DP(n,d) is the time bound for computing the dominance product for n points in \mathbb{R}^d.
That is a matrix D, such that
D[i,j] = \bigl| \{k \mid p_i[k] \leq p_j[k]\} \bigr|; this is the number of coordinates at which p_j dominates p_i.
For integer coordinates from some interval [-M, M], we obtain an algorithm that runs in \tilde{O}\left(\min\{Mn^{\omega(1,r,1)},\, DP(n,d)\}\right) time, where \omega(1,r,1) is the exponent of multiplying an n \times n^r matrix by an n^r \times n matrix.
We also give slightly better bounds for DP(n,d), by using more recent rectangular matrix multiplication bounds.
Computing the dominance product itself is an important task, since it is applied in many algorithms as a major black-box ingredient, such as algorithms for APBP (all pairs bottleneck paths),
and variants of APSP (all pairs shortest paths).
Cite as
Omer Gold and Micha Sharir. Dominance Product and High-Dimensional Closest Pair under L_infty. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 39:1-39:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{gold_et_al:LIPIcs.ISAAC.2017.39,
author = {Gold, Omer and Sharir, Micha},
title = {{Dominance Product and High-Dimensional Closest Pair under L\underlineinfty}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {39:1--39:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.39},
URN = {urn:nbn:de:0030-drops-82268},
doi = {10.4230/LIPIcs.ISAAC.2017.39},
annote = {Keywords: Closest Pair, Dominance Product, L\underlineinfty Proximity, Rectangular Matrix Multiplication}
}
Document
Orthogonal Vectors Indexing
Abstract
In the recent years, intensive research work has been dedicated to prove conditional lower bounds in order to reveal the inner structure of the class P. These conditional lower bounds are based on many popular conjectures on well-studied problems. One of the most heavily used conjectures is the celebrated Strong Exponential Time Hypothesis (SETH). It turns out that conditional hardness proved based on SETH goes, in many cases, through an intermediate problem - the Orthogonal Vectors (OV) problem.
Almost all research work regarding conditional lower bound was concentrated on time complexity. Very little attention was directed toward space complexity. In a recent work, Goldstein et al.[WADS '17] set the stage for proving conditional lower bounds regarding space and its interplay with time. In this spirit, it is tempting to investigate the space complexity of a data structure variant of OV which is called OV indexing. In this problem n boolean vectors of size clogn are given for preprocessing. As a query, a vector v is given and we are required to verify if there is an input vector that is orthogonal to it or not.
This OV indexing problem is interesting in its own, but it also likely to have strong implications on problems known to be conditionally hard, in terms of time complexity, based on OV. Having this in mind, we study OV indexing in this paper from many aspects. We give some space-efficient algorithms for the problem, show a tradeoff between space and query time, describe how to solve its reporting variant, shed light on an interesting connection between this problem and the well-studied SetDisjointness problem and demonstrate how it can be solved more efficiently on random input.
Cite as
Isaac Goldstein, Moshe Lewenstein, and Ely Porat. Orthogonal Vectors Indexing. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 40:1-40:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{goldstein_et_al:LIPIcs.ISAAC.2017.40,
author = {Goldstein, Isaac and Lewenstein, Moshe and Porat, Ely},
title = {{Orthogonal Vectors Indexing}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {40:1--40:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.40},
URN = {urn:nbn:de:0030-drops-82395},
doi = {10.4230/LIPIcs.ISAAC.2017.40},
annote = {Keywords: SETH, orthogonal vectors, space complexity}
}
Document
Non-approximability and Polylogarithmic Approximations of the Single-Sink Unsplittable and Confluent Dynamic Flow Problems
Abstract
Dynamic Flows were introduced by Ford and Fulkerson in 1958 to model flows over time. They define edge capacities to be the total amount of flow that can enter an edge in one time unit. Each edge also has a length, representing the time needed to traverse it. Dynamic Flows have been used to model many problems including traffic congestion, hop-routing of packets and evacuation protocols in buildings. While the basic problem of moving the maximal amount of supplies from sources to sinks is polynomial time solvable, natural minor modifications can make it NP-hard.
One such modification is that flows be confluent, i.e., all flows leaving a vertex must leave along the same edge. This corresponds to natural conditions in, e.g., evacuation planning and hop routing.
We investigate the single-sink Confluent Quickest Flow problem. The input is a graph with edge capacities and lengths, sources with supplies and a sink. The problem is to find a confluent flow minimizing the time required to send supplies to the sink. Our main results include:
a) Logarithmic Non-Approximability: Directed Confluent Quickest Flows cannot be approximated in polynomial time with an O(\log n) approximation factor, unless P=NP.
b) Polylogarithmic Bicriteria Approximations: Polynomial time (O(\log^8 n), O(\log^2 \kappa)) bicritera approximation algorithms for the Confluent Quickest Flow problem where \kappa is the number of sinks, in both directed and undirected graphs.
Corresponding results are also developed for the Confluent Maximum Flow over time problem. The techniques developed also improve recent approximation algorithms for static confluent flows.
Cite as
Mordecai J. Golin, Hadi Khodabande, and Bo Qin. Non-approximability and Polylogarithmic Approximations of the Single-Sink Unsplittable and Confluent Dynamic Flow Problems. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 41:1-41:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{golin_et_al:LIPIcs.ISAAC.2017.41,
author = {Golin, Mordecai J. and Khodabande, Hadi and Qin, Bo},
title = {{Non-approximability and Polylogarithmic Approximations of the Single-Sink Unsplittable and Confluent Dynamic Flow Problems}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {41:1--41:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.41},
URN = {urn:nbn:de:0030-drops-82435},
doi = {10.4230/LIPIcs.ISAAC.2017.41},
annote = {Keywords: Optimization, Approximation, Dynamic Flow, Confluent Flow}
}
Document
Range-Efficient Consistent Sampling and Locality-Sensitive Hashing for Polygons
Abstract
Locality-sensitive hashing (LSH) is a fundamental technique for similarity search and similarity estimation in high-dimensional spaces.
The basic idea is that similar objects should produce hash collisions with probability significantly larger than objects with low similarity.
We consider LSH for objects that can be represented as point sets in either one or two dimensions.
To make the point sets finite size we consider the subset of points on a grid.
Directly applying LSH (e.g. min-wise hashing) to these point sets would require time proportional to the number of points.
We seek to achieve time that is much lower than direct approaches.
Technically, we introduce new primitives for range-efficient consistent sampling (of independent interest), and show how to turn such samples into LSH values.
Another application of our technique is a data structure for quickly estimating the size of the intersection or union of a set of preprocessed polygons.
Curiously, our consistent sampling method uses transformation to a geometric problem.
Cite as
Joachim Gudmundsson and Rasmus Pagh. Range-Efficient Consistent Sampling and Locality-Sensitive Hashing for Polygons. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 42:1-42:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{gudmundsson_et_al:LIPIcs.ISAAC.2017.42,
author = {Gudmundsson, Joachim and Pagh, Rasmus},
title = {{Range-Efficient Consistent Sampling and Locality-Sensitive Hashing for Polygons}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {42:1--42:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.42},
URN = {urn:nbn:de:0030-drops-82316},
doi = {10.4230/LIPIcs.ISAAC.2017.42},
annote = {Keywords: Locality-sensitive hashing, probability distribution, polygon, min-wise hashing, consistent sampling}
}
Document
Maximum Induced Matching Algorithms via Vertex Ordering Characterizations
Abstract
We study the maximum induced matching problem on a graph G.
Induced matchings correspond to independent sets in L^2(G), the square of the line graph of G.
The problem is NP-complete on bipartite graphs.
In this work, we show that for a number of graph families with forbidden vertex orderings, almost all forbidden patterns on three vertices are preserved when taking the square of the line graph.
These orderings can be computed in linear time in the size of the input graph.
In particular, given a graph class \mathcal{G} characterized by a vertex ordering, and a graph G=(V,E) \in \mathcal{G} with a corresponding vertex ordering \sigma of V, one can produce (in linear time in the size of G) an ordering on the vertices of L^2(G), that shows that L^2(G) \in \mathcal{G} - for a number of graph classes \mathcal{G} - without computing the line graph or the square of the line graph of G.
These results generalize and unify previous ones on showing closure under L^2(\cdot) for various graph families.
Furthermore, these orderings on L^2(G) can be exploited algorithmically to compute a maximum induced matching on G faster. We illustrate this latter fact in the second half of the paper where we focus on cocomparability graphs, a large graph class that includes interval, permutation, trapezoid graphs, and co-graphs, and we present the first \mathcal{O}(mn) time algorithm to compute a maximum weighted induced matching on cocomparability graphs; an improvement from the best known \mathcal{O}(n^4) time algorithm for the unweighted case.
Cite as
Michel Habib and Lalla Mouatadid. Maximum Induced Matching Algorithms via Vertex Ordering Characterizations. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 43:1-43:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{habib_et_al:LIPIcs.ISAAC.2017.43,
author = {Habib, Michel and Mouatadid, Lalla},
title = {{Maximum Induced Matching Algorithms via Vertex Ordering Characterizations}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {43:1--43:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.43},
URN = {urn:nbn:de:0030-drops-82178},
doi = {10.4230/LIPIcs.ISAAC.2017.43},
annote = {Keywords: Maximum induced matching, Independent set, Vertex ordering charac- terization, Graph classes, Fast algorithms, Cocomparability graphs}
}
Document
On-the-Fly Array Initialization in Less Space
Abstract
We show that for all given n,t,w in {1,2,...} with n<2^w, an array of n entries of w bits each can be represented on a word RAM with a word length of w bits in at most nw+ceil(n(t/(2 w))^t) bits of uninitialized memory to support constant-time initialization of the whole array and O(t)-time reading and writing of individual array entries. At one end of this tradeoff, we achieve initialization and access (i.e., reading and writing) in constant time with nw+ceil(n/w^t) bits for arbitrary fixed t, to be compared with nw+Theta(n) bits for the best previous solution, and at the opposite end, still with constant-time initialization, we support O(log n)-time access with just nw+1 bits, which is optimal for arbitrary access times if the initialization executes fewer than n steps.
Cite as
Torben Hagerup and Frank Kammer. On-the-Fly Array Initialization in Less Space. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 44:1-44:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{hagerup_et_al:LIPIcs.ISAAC.2017.44,
author = {Hagerup, Torben and Kammer, Frank},
title = {{On-the-Fly Array Initialization in Less Space}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {44:1--44:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.44},
URN = {urn:nbn:de:0030-drops-82527},
doi = {10.4230/LIPIcs.ISAAC.2017.44},
annote = {Keywords: data structures, space efficiency, constant-time initialization, on-the-fly initialization, arrays}
}
Document
On Directed Covering and Domination Problems
Abstract
In this paper, we study covering and domination problems on directed graphs.
Although undirected Vertex Cover and Edge Dominating Set are well-studied classical graph problems, the directed versions have not been studied much due to the lack of clear definitions.
We give natural definitions for Directed r-In (Out) Vertex Cover and Directed (p,q)-Edge Dominating Set as directed generations of Vertex Cover and Edge Dominating Set.
For these problems, we show that
(1) Directed r-In (Out) Vertex Cover and Directed (p,q)-Edge Dominating Set are NP-complete on planar directed acyclic graphs except when r=1 or (p,q)=(0,0),
(2) if r>=2, Directed r-In (Out) Vertex Cover is W[2]-hard and (c*ln k)-inapproximable on directed acyclic graphs,
(3) if either p or q is greater than 1, Directed (p,q)-Edge Dominating Set is W[2]-hard and (c*ln k)-inapproximable on directed acyclic graphs,
(4) all problems can be solved in polynomial time on trees, and
(5) Directed (0,1),(1,0),(1,1)-Edge Dominating Set are fixed-parameter tractable in general graphs.
The first result implies that (directed) r-Dominating Set on directed line graphs is NP-complete even if r=1.
Cite as
Tesshu Hanaka, Naomi Nishimura, and Hirotaka Ono. On Directed Covering and Domination Problems. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 45:1-45:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{hanaka_et_al:LIPIcs.ISAAC.2017.45,
author = {Hanaka, Tesshu and Nishimura, Naomi and Ono, Hirotaka},
title = {{On Directed Covering and Domination Problems}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {45:1--45:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.45},
URN = {urn:nbn:de:0030-drops-82460},
doi = {10.4230/LIPIcs.ISAAC.2017.45},
annote = {Keywords: directed graph, vertex cover, dominating set, edge dominating set, fixed-parameter algorithms}
}
Document
Settlement Fund Circulation Problem
Abstract
In the economic activities,
the central bank has an important role to cover payments of banks,
when they are short of funds to clear their debts.
For this purpose, the central bank timely puts funds so that the economic activities go smooth.
Since payments in this mechanism are processed sequentially,
the total amount of funds put by the central bank critically
depends on the order of the payments.
Then an interest goes to the amount to prepare
if the order of the payments can be controlled by the central bank,
or if it is determined under the worst case scenario.
This motivates us to introduce a brand-new problem,
which we call the settlement fund circulation problem.
The problems are formulated as follows:
Let G=(V,A) be a directed multigraph with a vertex set V and an arc set A.
Each arc a\in A is endowed debt d(a)\ge 0,
and the debts are settled sequentially under a sequence \pi of arcs.
Each vertex v\in V is put fund in the amount of p_{\pi}(v)\ge 0
under the sequence.
The minimum/maximum settlement fund circulation problem (Min-SFC/Max-SFC)
in a given graph G with debts d: A\rightarrow \mathbb{R}_{+}\cup \{0\}
asks to find a bijection \pi:A\to \{1,2,\dots,|A|\}
that minimizes/maximizes the total funds \sum _{v\in V}p_{\pi }(v).
In this paper, we show that
both Min-SFC and Max-SFC are NP-hard;
in particular, Min-SFC is
(I) strongly NP-hard even if G is
(i) a multigraph with |V|=2 or (ii) a simple graph with treewidth at most two,and is (II) (not necessarily strongly) NP-hard for simple trees of diameter four,
while it is solvable in polynomial time for stars.
Also, we identify several polynomial time solvable cases for both problems.
Cite as
Hitoshi Hayakawa, Toshimasa Ishii, Hirotaka Ono, and Yushi Uno. Settlement Fund Circulation Problem. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 46:1-46:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{hayakawa_et_al:LIPIcs.ISAAC.2017.46,
author = {Hayakawa, Hitoshi and Ishii, Toshimasa and Ono, Hirotaka and Uno, Yushi},
title = {{Settlement Fund Circulation Problem}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {46:1--46:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.46},
URN = {urn:nbn:de:0030-drops-82351},
doi = {10.4230/LIPIcs.ISAAC.2017.46},
annote = {Keywords: Fund settlement, Algorithm, Digraph, Scheduling}
}
Document
An Efficient Sum Query Algorithm for Distance-based Locally Dominating Functions
Abstract
In this paper, we consider the following sum query problem:
Given a point set P in R^d, and a distance-based function f(p,q) (i.e. a function of the distance between p and q) satisfying some general properties,
the goal is to develop a data structure and a query algorithm for efficiently computing a (1+epsilon)-approximate solution to the sum
sum_{p in P} f(p,q) for any query point q in R^d and any small constant epsilon>0. Existing techniques for this problem are mainly based on some core-set techniques which often have difficulties to deal with functions with local domination property. Based on several new insights to this problem, we develop in this paper a novel technique to overcome these encountered difficulties. Our algorithm is capable of answering queries with high success probability in time no more than ~O_{epsilon,d}(n^{0.5 + c}), and the underlying
data structure can be constructed in ~O_{epsilon,d}(n^{1+c}) time for any c>0, where the hidden constant has only polynomial dependence on 1/epsilon and d.
Our technique is simple and can be easily implemented for practical purpose.
Cite as
Ziyun Huang and Jinhui Xu. An Efficient Sum Query Algorithm for Distance-based Locally Dominating Functions. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 47:1-47:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{huang_et_al:LIPIcs.ISAAC.2017.47,
author = {Huang, Ziyun and Xu, Jinhui},
title = {{An Efficient Sum Query Algorithm for Distance-based Locally Dominating Functions}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {47:1--47:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.47},
URN = {urn:nbn:de:0030-drops-82483},
doi = {10.4230/LIPIcs.ISAAC.2017.47},
annote = {Keywords: Sum Query, Distance-based Function, Local Domination, High Dimen- sions, Data Structure}
}
Document
Complexity of the Multi-Service Center Problem
Abstract
The multi-service center problem is a variant of facility location problems. In the problem, we consider locating p facilities on a graph, each of which provides distinct service required by all vertices. Each vertex incurs the cost determined by the sum of the weighted distances to the p facilities. The aim of the problem is to minimize the maximum cost among all vertices. This problem is known to be NP-hard for general graphs, while it is solvable in polynomial time when p is a fixed constant. In this paper, we give sharp analyses for the complexity of the problem from the viewpoint of graph classes and weights on vertices. We first propose a polynomial-time algorithm for trees when p is a part of input. In contrast, we prove that the problem becomes strongly NP-hard even for cycles. We also show that when vertices are allowed to have negative weights, the problem becomes NP-hard for paths of only three vertices and strongly NP-hard for stars.
Cite as
Takehiro Ito, Naonori Kakimura, and Yusuke Kobayashi. Complexity of the Multi-Service Center Problem. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 48:1-48:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{ito_et_al:LIPIcs.ISAAC.2017.48,
author = {Ito, Takehiro and Kakimura, Naonori and Kobayashi, Yusuke},
title = {{Complexity of the Multi-Service Center Problem}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {48:1--48:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.48},
URN = {urn:nbn:de:0030-drops-82536},
doi = {10.4230/LIPIcs.ISAAC.2017.48},
annote = {Keywords: facility location, graph algorithm, multi-service location}
}
Document
Improved Algorithms for Scheduling Unsplittable Flows on Paths
Abstract
In this paper, we investigate offline and online algorithms for Round-UFPP, the problem of minimizing the number of rounds required to schedule a set of unsplittable flows of non-uniform sizes
on a given path with non-uniform edge capacities. Round-UFPP is NP-hard and constant-factor approximation algorithms are known under the no bottleneck assumption (NBA), which stipulates that maximum size of a flow is at most the minimum edge capacity. We study Round-UFPP
without the NBA, and present improved online and offline algorithms. We first study offline Round-UFPP for a restricted class of instances called alpha-small, where the size of each flow is at
most alpha times the capacity of its bottleneck edge, and present an O(log(1/(1 - alpha)))-approximation algorithm. Our main result is an online O(log log cmax)-competitive algorithm for Round-UFPP
for general instances, where cmax is the largest edge capacities, improving upon the previous best bound of O(log cmax) due to [16]. Our result leads to an offline O(min(log n, log m, log log cmax))-
approximation algorithm and an online O(min(log m, log log cmax))-competitive algorithm for Round-UFPP, where n is the number of flows and m is the number of edges.
Cite as
Hamidreza Jahanjou, Erez Kantor, and Rajmohan Rajaraman. Improved Algorithms for Scheduling Unsplittable Flows on Paths. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 49:1-49:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{jahanjou_et_al:LIPIcs.ISAAC.2017.49,
author = {Jahanjou, Hamidreza and Kantor, Erez and Rajaraman, Rajmohan},
title = {{Improved Algorithms for Scheduling Unsplittable Flows on Paths}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {49:1--49:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.49},
URN = {urn:nbn:de:0030-drops-82292},
doi = {10.4230/LIPIcs.ISAAC.2017.49},
annote = {Keywords: Approximation algorithms, Online algorithms, Unsplittable flows, Interval coloring, Flow scheduling}
}
Document
Structural Parameters, Tight Bounds, and Approximation for (k,r)-Center
Abstract
In (k,r)-Center we are given a (possibly edge-weighted) graph and are asked to select at most k vertices (centers), so that all other vertices are at distance at most r from a center. In this paper we provide a number of tight fine-grained bounds on the complexity of this problem with respect to various standard graph parameters. Specifically:
- For any r>=1, we show an algorithm that solves the problem in O*((3r+1)^cw) time, where cw is the clique-width of the input graph, as well as a tight SETH lower bound matching this algorithm's performance. As a corollary, for r=1, this closes the gap that previously existed on the complexity of Dominating Set parameterized by cw.
- We strengthen previously known FPT lower bounds, by showing that (k,r)-Center is W[1]-hard parameterized by the input graph's vertex cover (if edge weights are allowed), or feedback vertex set, even if k is an additional parameter. Our reductions imply tight ETH-based lower bounds. Finally, we devise an algorithm parameterized by vertex cover for unweighted graphs.
- We show that the complexity of the problem parameterized by tree-depth is 2^Theta(td^2) by showing an algorithm of this complexity and a tight ETH-based lower bound.
We complement these mostly negative results by providing FPT approximation schemes parameterized by clique-width or treewidth which work efficiently independently of the values of k,r. In particular, we give algorithms which, for any epsilon>0, run in time O*((tw/epsilon)^O(tw)), O*((cw/epsilon)^O(cw)) and return a (k,(1+epsilon)r)-center, if a (k,r)-center exists, thus circumventing the problem's W-hardness.
Cite as
Ioannis Katsikarelis, Michael Lampis, and Vangelis Th. Paschos. Structural Parameters, Tight Bounds, and Approximation for (k,r)-Center. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 50:1-50:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{katsikarelis_et_al:LIPIcs.ISAAC.2017.50,
author = {Katsikarelis, Ioannis and Lampis, Michael and Paschos, Vangelis Th.},
title = {{Structural Parameters, Tight Bounds, and Approximation for (k,r)-Center}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {50:1--50:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.50},
URN = {urn:nbn:de:0030-drops-82441},
doi = {10.4230/LIPIcs.ISAAC.2017.50},
annote = {Keywords: FPT algorithms, Approximation, Treewidth, Clique-width, Domination}
}
Document
Optimal Matroid Partitioning Problems
Abstract
This paper studies optimal matroid partitioning problems for various objective functions. In the problem, we are given a finite set E and k weighted matroids (E, \mathcal{I}_i, w_i), i = 1, \dots, k, and our task is to find a minimum partition (I_1,\dots,I_k) of E such that I_i \in \mathcal{I}_i for all i. For each objective function, we give a polynomial-time algorithm or prove NP-hardness. In particular, for the case when the given weighted matroids are identical and the objective function is the sum of the maximum weight in each set (i.e., \sum_{i=1}^k\max_{e\in I_i}w_i(e)), we show that the problem is strongly NP-hard but admits a PTAS.
Cite as
Yasushi Kawase, Kei Kimura, Kazuhisa Makino, and Hanna Sumita. Optimal Matroid Partitioning Problems. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 51:1-51:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{kawase_et_al:LIPIcs.ISAAC.2017.51,
author = {Kawase, Yasushi and Kimura, Kei and Makino, Kazuhisa and Sumita, Hanna},
title = {{Optimal Matroid Partitioning Problems}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {51:1--51:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.51},
URN = {urn:nbn:de:0030-drops-82712},
doi = {10.4230/LIPIcs.ISAAC.2017.51},
annote = {Keywords: Matroids, Partitioning problem, PTAS, NP-hardness}
}
Document
Improved Bounds for Online Dominating Sets of Trees
Abstract
The online dominating set problem is an online variant of the minimum dominating set problem, which is one of the most important NP-hard problems on graphs. This problem is defined as follows: Given an undirected graph G = (V, E), in which V is a set of vertices and E is a set of edges. We say that a set D \subseteq V of vertices is a dominating set of G if for each v \in V \setminus D, there exists a vertex u \in D such that {u, v} \in E. The vertices are revealed to an online algorithm one by one over time. When a vertex is revealed, edges between the vertex and vertices revealed in the past are also revealed. A revelaed subtree is connected at any time. Immediately after the revelation of each vertex, an online algorithm can choose vertices which were already revealed irrevocably and must maintain a dominating set of a graph revealed so far. The cost of an algorithm on a given tree is the number of vertices chosen by it, and its objective is to minimize the cost. Eidenbenz (Technical report, Institute of Theoretical Computer Science, ETH Zurich, 2002) and Boyar et al. (SWAT 2016) studied the case in which given graphs are trees. They designed a deterministic online algorithm whose competitive ratio is at most three, and proved that a lower bound on the competitive ratio of any deterministic algorithm is two.
In this paper, we also focus on trees. We establish a matching lower bound for any deterministic algorithm. Moreover, we design a randomized online algorithm whose competitive ratio is at most 5/2 = 2.5, and show that the competitive ratio of any randomized algorithm is at least 4/3 \approx 1.333.
Cite as
Koji M. Kobayashi. Improved Bounds for Online Dominating Sets of Trees. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 52:1-52:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{kobayashi:LIPIcs.ISAAC.2017.52,
author = {Kobayashi, Koji M.},
title = {{Improved Bounds for Online Dominating Sets of Trees}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {52:1--52:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.52},
URN = {urn:nbn:de:0030-drops-82364},
doi = {10.4230/LIPIcs.ISAAC.2017.52},
annote = {Keywords: online algorithm, dominating set, competitive analysis, tree graph, randomized algorithm}
}
Document
Maximizing the Strong Triadic Closure in Split Graphs and Proper Interval Graphs
Abstract
In social networks the Strong Triadic Closure is an assignment of the edges with strong or weak labels such that any two vertices that have a common neighbor with a strong edge are adjacent. The problem of maximizing the number of strong edges that satisfy the strong triadic closure was recently shown to be NP-complete for general graphs. Here we initiate the study of graph classes for which the problem is solvable. We show that the problem admits a polynomial-time algorithm for two unrelated classes of graphs: proper interval graphs and trivially-perfect graphs. To complement our result, we show that the problem remains NP-complete on split graphs, and consequently also on chordal graphs. Thus we contribute to define the first border between graph classes on which the problem is polynomially solvable and on which it remains NP-complete.
Cite as
Athanasios L. Konstantinidis and Charis Papadopoulos. Maximizing the Strong Triadic Closure in Split Graphs and Proper Interval Graphs. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 53:1-53:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{konstantinidis_et_al:LIPIcs.ISAAC.2017.53,
author = {Konstantinidis, Athanasios L. and Papadopoulos, Charis},
title = {{Maximizing the Strong Triadic Closure in Split Graphs and Proper Interval Graphs}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {53:1--53:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.53},
URN = {urn:nbn:de:0030-drops-82113},
doi = {10.4230/LIPIcs.ISAAC.2017.53},
annote = {Keywords: strong triadic closure, polynomial-time algorithm, NP-completeness, split graphs, proper interval graphs}
}
Document
Non-Crossing Geometric Steiner Arborescences
Abstract
Motivated by the question of simultaneous embedding of several flow maps, we consider the problem of drawing multiple geometric Steiner arborescences with no crossings in the rectilinear and in the angle-restricted setting. When terminal-to-root paths are allowed to turn freely, we show that two rectilinear Steiner arborescences have a non-crossing drawing if neither tree necessarily completely disconnects the other tree and if the roots of both trees are "free". If the roots are not free, then we can reduce the decision problem to 2SAT. If terminal-to-root paths are allowed to turn only at Steiner points, then it is NP-hard to decide whether multiple rectilinear Steiner arborescences have a non-crossing drawing. The setting of angle-restricted Steiner arborescences is more subtle than the rectilinear case. Our NP-hardness result extends, but testing whether there exists a non-crossing drawing if the roots of both trees are free requires additional conditions to be fulfilled.
Cite as
Irina Kostitsyna, Bettina Speckmann, and Kevin Verbeek. Non-Crossing Geometric Steiner Arborescences. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 54:1-54:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{kostitsyna_et_al:LIPIcs.ISAAC.2017.54,
author = {Kostitsyna, Irina and Speckmann, Bettina and Verbeek, Kevin},
title = {{Non-Crossing Geometric Steiner Arborescences}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {54:1--54:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.54},
URN = {urn:nbn:de:0030-drops-82342},
doi = {10.4230/LIPIcs.ISAAC.2017.54},
annote = {Keywords: Steiner arborescences, non-crossing drawing, rectilinear, angle-restricted}
}
Document
Precedence-Constrained Min Sum Set Cover
Abstract
We introduce a version of the Min Sum Set Cover (MSSC) problem in which there are "AND" precedence constraints on the m sets. In the Precedence-Constrained Min Sum Set Cover (PCMSSC) problem, when interpreted as directed edges, the constraints induce an acyclic directed graph. PCMSSC models the aim of scheduling software tests to prioritize the rate of fault detection subject to dependencies between tests.
Our greedy scheme for PCMSSC is similar to the approaches of Feige, Lovasz, and, Tetali for MSSC, and Chekuri and Motwani for precedence-constrained scheduling to minimize weighted completion time. With a factor-4 increase in approximation ratio, we reduce PCMSSC to the problem of
finding a maximum-density precedence-closed sub-family of sets, where density is the ratio of sub-family union size to cardinality. We provide a greedy factor-sqrt m algorithm for maximizing density; on forests of in-trees, we show this algorithm finds an optimal solution. Harnessing an alternative greedy argument of Chekuri and Kumar for Maximum Coverage with Group Budget Constraints, on forests of out-trees, we design an algorithm with approximation ratio equal to maximum tree height.
Finally, with a reduction from the Planted Dense Subgraph detection problem, we show that its conjectured hardness implies there is no polynomial-time algorithm for PCMSSC with approximation factor in O(m^{1/12-epsilon}).
Cite as
Jessica McClintock, Julián Mestre, and Anthony Wirth. Precedence-Constrained Min Sum Set Cover. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 55:1-55:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{mcclintock_et_al:LIPIcs.ISAAC.2017.55,
author = {McClintock, Jessica and Mestre, Juli\'{a}n and Wirth, Anthony},
title = {{Precedence-Constrained Min Sum Set Cover}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {55:1--55:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.55},
URN = {urn:nbn:de:0030-drops-82648},
doi = {10.4230/LIPIcs.ISAAC.2017.55},
annote = {Keywords: planted dense subgraph, min sum set cover, precedence constrained}
}
Document
Jointly Stable Matchings
Abstract
In the stable marriage problem, we are given a set of men, a set of women, and each person's preference list. Our task is to find a stable matching, that is, a matching admitting no unmatched (man, woman)-pair each of which improves the situation by being matched together. It is known that any instance admits at least one stable matching. In this paper, we consider a natural extension where k (>= 2) sets of preference lists L_i (1 <= i <= k) over the same set of people are given, and the aim is to find a jointly stable matching, a matching that is stable with respect to all L_i. We show that the decision problem is NP-complete already for k=2, even if each person's preference list is of length at most four, while it is solvable in linear time for any k if each man's preference list is of length at most two (women's lists can be of unbounded length). We also show that if each woman's preference lists are same in all L_i, then the problem can be solved in linear time.
Cite as
Shuichi Miyazaki and Kazuya Okamoto. Jointly Stable Matchings. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 56:1-56:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{miyazaki_et_al:LIPIcs.ISAAC.2017.56,
author = {Miyazaki, Shuichi and Okamoto, Kazuya},
title = {{Jointly Stable Matchings}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {56:1--56:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.56},
URN = {urn:nbn:de:0030-drops-82244},
doi = {10.4230/LIPIcs.ISAAC.2017.56},
annote = {Keywords: stable marriage problem, stable matching, NP-completeness, linear time algorithm}
}
Document
Fast Compressed Self-Indexes with Deterministic Linear-Time Construction
Abstract
We introduce a compressed suffix array representation that, on a text T of length n over an alphabet of size \sigma, can be built in O(n) deterministic time, within O(n\log\sigma) bits of working space, and counts the number of occurrences of any pattern P in T in time O(|P| + \log\log_w \sigma) on a RAM machine of w=\Omega(\log n)-bit words. This new index outperforms all the other compressed indexes that can be built in linear deterministic time, and some others. The only faster indexes can be built in linear time only in expectation, or require \Theta(n\log n) bits.
Cite as
J. Ian Munro, Gonzalo Navarro, and Yakov Nekrich. Fast Compressed Self-Indexes with Deterministic Linear-Time Construction. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 57:1-57:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{munro_et_al:LIPIcs.ISAAC.2017.57,
author = {Munro, J. Ian and Navarro, Gonzalo and Nekrich, Yakov},
title = {{Fast Compressed Self-Indexes with Deterministic Linear-Time Construction}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {57:1--57:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.57},
URN = {urn:nbn:de:0030-drops-82328},
doi = {10.4230/LIPIcs.ISAAC.2017.57},
annote = {Keywords: Succinct data structures, Self-indexes, Suffix arrays, Deterministic construction}
}
Document
Satisfiability Algorithm for Syntactic Read-$k$-times Branching Programs
Abstract
The satisfiability of a given branching program is to determine whether there exists a consistent path from the root to 1-sink.
In a syntactic read-k-times branching program, each variable appears at most k times in any path from the root to a sink.
We provide a satisfiability algorithm for syntactic read-k-times branching programs with n variables and m edges that runs in time O\left(\poly(n, m^{k^2})\cdot 2^{(1-\mu(k))n}\right), where \mu(k) = \frac{1}{4^{k+1}}. Our algorithm is based on the decomposition technique shown by Borodin, Razborov and Smolensky [Computational Complexity, 1993].
Cite as
Atsuki Nagao, Kazuhisa Seto, and Junichi Teruyama. Satisfiability Algorithm for Syntactic Read-$k$-times Branching Programs. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 58:1-58:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{nagao_et_al:LIPIcs.ISAAC.2017.58,
author = {Nagao, Atsuki and Seto, Kazuhisa and Teruyama, Junichi},
title = {{Satisfiability Algorithm for Syntactic Read-\$k\$-times Branching Programs}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {58:1--58:10},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.58},
URN = {urn:nbn:de:0030-drops-82423},
doi = {10.4230/LIPIcs.ISAAC.2017.58},
annote = {Keywords: branching program, read-k-times, satisfiability, moderately exponential time, polynomial space}
}
Document
Fully Dynamic Connectivity Oracles under General Vertex Updates
Abstract
We study the following dynamic graph problem: given an undirected graph G, we maintain a connectivity oracle between any two vertices in G under any on-line sequence of vertex deletions and insertions with incident edges. We propose two algorithms for this problem: an amortized update time deterministic one and a worst case update time Monte Carlo one.
Both of them allow an arbitrary number of new vertices to insert.
The update time complexity of the former algorithm is no worse than the existing algorithms, which allow only limited number of vertices to insert.
Moreover, for relatively dense graphs, we can expect that the update time bound of the former algorithm meets a lower bound,
and that of the latter algorithm can be seen as a substantial improvement of the existing result by introducing randomization.
Cite as
Kengo Nakamura. Fully Dynamic Connectivity Oracles under General Vertex Updates. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 59:1-59:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{nakamura:LIPIcs.ISAAC.2017.59,
author = {Nakamura, Kengo},
title = {{Fully Dynamic Connectivity Oracles under General Vertex Updates}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {59:1--59:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.59},
URN = {urn:nbn:de:0030-drops-82607},
doi = {10.4230/LIPIcs.ISAAC.2017.59},
annote = {Keywords: Dynamic Graph, Connectivity, Depth-First Search}
}
Document
Finding Pairwise Intersections of Rectangles in a Query Rectangle
Abstract
We consider the following problem: Preprocess a set S of n axis-parallel boxes in \mathbb{R}^d so that given a query of an axis-parallel box Q in \mathbb{R}^d, the pairs of boxes of S whose intersection intersects the query box can be reported efficiently. For the case that d=2, we present a data structure of size O(n\log n) supporting O(\log n+k) query time, where k is the size of the output. This improves the previously best known result by de Berg et al. which requires O(\log n\log^* n+ k\log n) query time using O(n\log n) space.There has been no known result for this problem for higher dimensions, except that for d=3, the best known data structure supports
O(\sqrt{n}+k\log^2\log^* n) query time using O(n\sqrt {n}\log n) space. For a constant d>2, we present a data structure supporting O(n^{1-\delta}\log^{d-1} n + k \polylog n) query time for any constant 1/d\leq\delta<1.The size of the data structure is O(n^{\delta d}\log n) if 1/d\leq\delta<1/2, or O(n^{\delta d-2\delta+1}) if 1/2\leq \delta<1.
Cite as
Eunjin Oh and Hee-Kap Ahn. Finding Pairwise Intersections of Rectangles in a Query Rectangle. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 60:1-60:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{oh_et_al:LIPIcs.ISAAC.2017.60,
author = {Oh, Eunjin and Ahn, Hee-Kap},
title = {{Finding Pairwise Intersections of Rectangles in a Query Rectangle}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {60:1--60:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.60},
URN = {urn:nbn:de:0030-drops-82417},
doi = {10.4230/LIPIcs.ISAAC.2017.60},
annote = {Keywords: Geometric data structures, axis-parallel rectangles, intersection}
}
Document
A New Balanced Subdivision of a Simple Polygon for Time-Space Trade-off Algorithms
Abstract
We are given a read-only memory for input and a write-only stream for output. For a positive integer parameter s, an s-workspace algorithm is an algorithm using only O(s) words of workspace in addition to the memory for input. In this paper, we present an O(n^2/s)-time s-workspace algorithm for subdividing a simple polygon into O(\min\{n/s,s\}) subpolygons of complexity O(\max\{n/s,s\}).
As applications of the subdivision, the previously best known time-space trade-offs for the following three geometric problems are improved immediately: (1) computing the shortest path between two points inside a simple n-gon, (2) computing the shortest path tree from a point inside a simple n-gon, (3) computing a triangulation of a simple n-gon. In addition, we improve the algorithm for the second problem even further.
Cite as
Eunjin Oh and Hee-Kap Ahn. A New Balanced Subdivision of a Simple Polygon for Time-Space Trade-off Algorithms. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 61:1-61:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{oh_et_al:LIPIcs.ISAAC.2017.61,
author = {Oh, Eunjin and Ahn, Hee-Kap},
title = {{A New Balanced Subdivision of a Simple Polygon for Time-Space Trade-off Algorithms}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {61:1--61:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.61},
URN = {urn:nbn:de:0030-drops-82401},
doi = {10.4230/LIPIcs.ISAAC.2017.61},
annote = {Keywords: Time-space trade-off, simple polygon, shortest path, shortest path tree}
}
Document
Complexity of Coloring Reconfiguration under Recolorability Constraints
Abstract
For an integer k \ge 1, k-coloring reconfiguration is one of the most well-studied reconfiguration problems, defined as follows: In the problem, we are given two (vertex-)colorings of a graph using k colors, and asked to transform one into the other by recoloring only one vertex at a time, while at all times maintaining a proper coloring. The problem is known to be PSPACE-complete if k \ge 4, and solvable for any graph in polynomial time if k \le 3. In this paper, we introduce a recolorability constraint on the k colors, which forbids some pairs of colors to be recolored directly. The recolorability constraint is given in terms of an undirected graph R such that each node in R corresponds to a color and each edge in R represents a pair of colors that can be recolored directly. We study the hardness of the problem based on the structure of recolorability constraints R. More specifically, we prove that the problem is PSPACE-complete if R is of maximum degree at least four, or has a connected component containing more than one cycle.
Cite as
Hiroki Osawa, Akira Suzuki, Takehiro Ito, and Xiao Zhou. Complexity of Coloring Reconfiguration under Recolorability Constraints. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 62:1-62:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{osawa_et_al:LIPIcs.ISAAC.2017.62,
author = {Osawa, Hiroki and Suzuki, Akira and Ito, Takehiro and Zhou, Xiao},
title = {{Complexity of Coloring Reconfiguration under Recolorability Constraints}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {62:1--62:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.62},
URN = {urn:nbn:de:0030-drops-82588},
doi = {10.4230/LIPIcs.ISAAC.2017.62},
annote = {Keywords: combinatorial reconfiguration, graph coloring, PSPACE-complete}
}
Document
Approximate Nearest Neighbors Search Without False Negatives For l_2 For c>sqrt{loglog{n}}
Abstract
In this paper, we report progress on answering the open problem presented by Pagh [11], who considered the near neighbor search without false negatives for the Hamming distance. We show new data structures for solving the c-approximate near neighbors problem without false negatives for Euclidean high dimensional space
\mathcal{R}^d. These data structures work for any c = \omega(\sqrt{\log{\log{n}}}), where n is the number of points in the input set, with poly-logarithmic query time and polynomial
pre-processing time. This improves over the known algorithms, which require c to be \Omega(\sqrt{d}).
This improvement is obtained by applying a sequence of reductions, which are interesting on their own. First, we reduce the problem to d instances of dimension logarithmic in n. Next, these instances are reduced to a number of c-approximate near neighbor search without false negatives instances in \big(\Rspace^k\big)^L space equipped with metric m(x,y) = \max_{1 \le i \leL}(\dist{x_i - y_i}_2).
Cite as
Piotr Sankowski and Piotr Wygocki. Approximate Nearest Neighbors Search Without False Negatives For l_2 For c>sqrt{loglog{n}}. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 63:1-63:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{sankowski_et_al:LIPIcs.ISAAC.2017.63,
author = {Sankowski, Piotr and Wygocki, Piotr},
title = {{Approximate Nearest Neighbors Search Without False Negatives For l\underline2 For c\ranglesqrt\{loglog\{n\}\}}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {63:1--63:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.63},
URN = {urn:nbn:de:0030-drops-82189},
doi = {10.4230/LIPIcs.ISAAC.2017.63},
annote = {Keywords: locality sensitive hashing, approximate near neighbor search, high- dimensional, similarity search}
}
Document
Tight Approximation for Partial Vertex Cover with Hard Capacities
Abstract
We consider the partial vertex cover problem with hard capacity constraints (Partial VC-HC) on hypergraphs. In this problem we are given a hypergraph G=(V,E) with a maximum edge size f and a covering requirement R. Each edge is associated with a demand, and each vertex is associated with a capacity and an (integral) available multiplicity. The objective is to compute a minimum vertex multiset such that at least R units of demand from the edges are covered by the capacities of the vertices in the multiset and the multiplicity of each vertex does not exceed its available multiplicity.
In this paper we present an f-approximation for this problem, improving over a previous result of (2f+2)(1+epsilon) by Cheung et al to the tight extent possible. Our new ingredient of this work is a generalized analysis on the extreme points of the natural LP, developed from previous works, and a strengthened LP lower-bound obtained for the optimal solutions.
Cite as
Jia-Yau Shiau, Mong-Jen Kao, Ching-Chi Lin, and D. T. Lee. Tight Approximation for Partial Vertex Cover with Hard Capacities. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 64:1-64:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{shiau_et_al:LIPIcs.ISAAC.2017.64,
author = {Shiau, Jia-Yau and Kao, Mong-Jen and Lin, Ching-Chi and Lee, D. T.},
title = {{Tight Approximation for Partial Vertex Cover with Hard Capacities}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {64:1--64:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.64},
URN = {urn:nbn:de:0030-drops-82694},
doi = {10.4230/LIPIcs.ISAAC.2017.64},
annote = {Keywords: Approximation Algorithm, Capacitated Vertex Cover, Hard Capacities}
}
Document
Hybrid VCSPs with Crisp and Valued Conservative Templates
Abstract
A constraint satisfaction problem (CSP) is a problem of computing a homomorphism R -> G between two relational structures, e.g. between two directed graphs.
Analyzing its complexity has been a very fruitful research direction, especially for fixed template CSPs (or, non-uniform CSPs), denoted CSP(G),
in which the right side structure G is fixed and the left side structure R is unconstrained.
Recently, the hybrid setting, written CSP_H(G), where both sides are restricted simultaneously, attracted some attention.
It assumes that R is taken from a class of relational structures H (called the structural restriction) that additionally is closed under inverse homomorphisms. The last property allows to exploit an algebraic machinery that has been developed for fixed template CSPs. The key concept that connects hybrid CSPs with fixed-template CSPs is the so called lifted language. Namely, this is a constraint language G_R that can be constructed from an input R. The tractability of the language G_R for any input R from H is a necessary condition for the tractability of the hybrid problem.
In the first part we investigate templates G for which the latter condition is not only necessary, but also is sufficient. We call such templates G widely tractable. For this purpose, we construct from G a new finite relational structure G' and define a maximal structural restriction H_0 as a class of structures homomorphic to G'.
For the so called strongly BJK templates that probably captures all templates, we prove that wide tractability is equivalent to the tractability of CSP_{H_0}(G).
Our proof is based on the key observation that R is homomorphic to G' if and only if the core of G_R is preserved by a Siggers polymorphism.
Analogous result is shown for conservative valued CSPs.
Cite as
Rustem Takhanov. Hybrid VCSPs with Crisp and Valued Conservative Templates. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 65:1-65:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{takhanov:LIPIcs.ISAAC.2017.65,
author = {Takhanov, Rustem},
title = {{Hybrid VCSPs with Crisp and Valued Conservative Templates}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {65:1--65:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.65},
URN = {urn:nbn:de:0030-drops-82474},
doi = {10.4230/LIPIcs.ISAAC.2017.65},
annote = {Keywords: constraint satisfaction problem, polymorphisms, algebraic approach, lifted language, hybrid CSPs, closed under inverse homomorphisms}
}
Document
A (1.4 + epsilon)-Approximation Algorithm for the 2-Max-Duo Problem
Abstract
The maximum duo-preservation string mapping (Max-Duo) problem is
the complement of the well studied minimum common string partition (MCSP) problem, both of which have applications in many fields including text compression and bioinformatics. k-Max-Duo is the restricted version of Max-Duo, where every letter of the alphabet occurs at most k times in each of the strings, which is readily reduced into the well known maximum independent set (MIS) problem on a graph of maximum degree \Delta \le 6(k-1). In particular, 2-Max-Duo can then be approximated arbitrarily close to 1.8 using the state-of-the-art approximation algorithm for the MIS problem. 2-Max-Duo was proved APX-hard and very recently a (1.6 + \epsilon)-approximation was claimed, for any \epsilon > 0. In this paper, we present a vertex-degree reduction technique, based on which, we show that 2-Max-Duo can be approximated arbitrarily close to 1.4.
Cite as
Yao Xu, Yong Chen, Guohui Lin, Tian Liu, Taibo Luo, and Peng Zhang. A (1.4 + epsilon)-Approximation Algorithm for the 2-Max-Duo Problem. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 66:1-66:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{xu_et_al:LIPIcs.ISAAC.2017.66,
author = {Xu, Yao and Chen, Yong and Lin, Guohui and Liu, Tian and Luo, Taibo and Zhang, Peng},
title = {{A (1.4 + epsilon)-Approximation Algorithm for the 2-Max-Duo Problem}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {66:1--66:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.66},
URN = {urn:nbn:de:0030-drops-82120},
doi = {10.4230/LIPIcs.ISAAC.2017.66},
annote = {Keywords: Approximation algorithm, duo-preservation string mapping, string partition, independent set}
}
Document
Envy-free Matchings with Lower Quotas
Abstract
While every instance of the Hospitals/Residents problem admits a stable matching, the problem with lower quotas (HR-LQ) has instances with no stable matching. For such an instance, we expect the existence of an envy-free matching, which is a relaxation of a stable matching preserving a kind of fairness property.
In this paper, we investigate the existence of an envy-free matching in several settings, in which hospitals have lower quotas. We first provide an algorithm that decides whether a given HR-LQ instance has an envy-free matching or not. Then, we consider envy-freeness in the Classified Stable Matching model due to Huang (2010), i.e., each hospital has lower and upper quotas on subsets of doctors. We show that, for this model, deciding the existence of an envy-free matching is NP-hard in general, but solvable in polynomial time if quotas are paramodular.
Cite as
Yu Yokoi. Envy-free Matchings with Lower Quotas. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 67:1-67:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
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@InProceedings{yokoi:LIPIcs.ISAAC.2017.67,
author = {Yokoi, Yu},
title = {{Envy-free Matchings with Lower Quotas}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {67:1--67:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Okamoto, Yoshio and Tokuyama, Takeshi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.67},
URN = {urn:nbn:de:0030-drops-82205},
doi = {10.4230/LIPIcs.ISAAC.2017.67},
annote = {Keywords: stable matchings, envy-free matchings, lower quotas, polynomial time algorithm, paramodular functions}
}