89 Search Results for "Sohler, Christian"

Volume

LIPIcs, Volume 87

25th Annual European Symposium on Algorithms (ESA 2017)

ESA 2017, September 4-6, 2017, Vienna, Austria

Editors: Kirk Pruhs and Christian Sohler

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.50
Connected k-Center and k-Diameter Clustering

Authors: Lukas Drexler, Jan Eube, Kelin Luo, Heiko Röglin, Melanie Schmidt, and Julian Wargalla

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
Motivated by an application from geodesy, we study the connected k-center problem and the connected k-diameter problem. These problems arise from the classical k-center and k-diameter problems by adding a side constraint. For the side constraint, we are given an undirected connectivity graph G on the input points, and a clustering is now only feasible if every cluster induces a connected subgraph in G. Usually in clustering problems one assumes that the clusters are pairwise disjoint. We study this case but additionally also the case that clusters are allowed to be non-disjoint. This can help to satisfy the connectivity constraints. Our main result is an O(1)-approximation algorithm for the disjoint connected k-center and k-diameter problem for Euclidean spaces of low dimension (constant d) and for metrics with constant doubling dimension. For general metrics, we get an O(log²k)-approximation. Our algorithms work by computing a non-disjoint connected clustering first and transforming it into a disjoint connected clustering. We complement these upper bounds by several upper and lower bounds for variations and special cases of the model.
Cite as

Lukas Drexler, Jan Eube, Kelin Luo, Heiko Röglin, Melanie Schmidt, and Julian Wargalla. Connected k-Center and k-Diameter Clustering. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 50:1-50:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{drexler_et_al:LIPIcs.ICALP.2023.50,
  author =	{Drexler, Lukas and Eube, Jan and Luo, Kelin and R\"{o}glin, Heiko and Schmidt, Melanie and Wargalla, Julian},
  title =	{{Connected k-Center and k-Diameter Clustering}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{50:1--50:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.50},
  URN =		{urn:nbn:de:0030-drops-181024},
  doi =		{10.4230/LIPIcs.ICALP.2023.50},
  annote =	{Keywords: Approximation algorithms, Clustering, Connectivity constraints}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.28
A Sublinear Local Access Implementation for the Chinese Restaurant Process

Authors: Peter Mörters, Christian Sohler, and Stefan Walzer

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
The Chinese restaurant process is a stochastic process closely related to the Dirichlet process that groups sequentially arriving objects into a variable number of classes, such that within each class objects are cyclically ordered. A popular description involves a restaurant, where customers arrive one by one and either sit down next to a randomly chosen customer at one of the existing tables or open a new table. The full state of the process after n steps is given by a permutation of the n objects and cannot be represented in sublinear space. In particular, if we only need specific information about a few objects or classes it would be preferable to obtain the answers without simulating the process completely. A recent line of research [Oded Goldreich et al., 2010; Moni Naor and Asaf Nussboim, 2007; Amartya Shankha Biswas et al., 2020; Guy Even et al., 2021] attempts to provide access to huge random objects without fully instantiating them. Such local access implementations provide answers to a sequence of queries about the random object, following the same distribution as if the object was fully generated. In this paper, we provide a local access implementation for a generalization of the Chinese restaurant process described above. Our implementation can be used to answer any sequence of adaptive queries about class affiliation of objects, number and sizes of classes at any time, position of elements within a class, or founding time of a class. The running time per query is polylogarithmic in the total size of the object, with high probability. Our approach relies on some ideas from the recent local access implementation for preferential attachment trees by Even et al. [Guy Even et al., 2021]. Such trees are related to the Chinese restaurant process in the sense that both involve a "rich-get-richer" phenomenon. A novel ingredient in our implementation is to embed the process in continuous time, in which the evolution of the different classes becomes stochastically independent [Joyce and Tavaré, 1987]. This independence is used to keep the probabilistic structure manageable even if many queries have already been answered. As similar embeddings are available for a wide range of urn processes [Krishna B. Athreya and Samuel Karlin, 1968], we believe that our approach may be applicable more generally. Moreover, local access implementations for birth and death processes that we encounter along the way may be of independent interest.
Cite as

Peter Mörters, Christian Sohler, and Stefan Walzer. A Sublinear Local Access Implementation for the Chinese Restaurant Process. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{morters_et_al:LIPIcs.APPROX/RANDOM.2022.28,
  author =	{M\"{o}rters, Peter and Sohler, Christian and Walzer, Stefan},
  title =	{{A Sublinear Local Access Implementation for the Chinese Restaurant Process}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{28:1--28:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.28},
  URN =		{urn:nbn:de:0030-drops-171500},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.28},
  annote =	{Keywords: Chinese restaurant process, Dirichlet process, sublinear time algorithm, random recursive tree, random permutation, random partition, Ewens distribution, simulation, local access implementation, continuous time embedding}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.16
Testable Properties in General Graphs and Random Order Streaming

Authors: Artur Czumaj, Hendrik Fichtenberger, Pan Peng, and Christian Sohler

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract
We consider the fundamental question of understanding the relative power of two important computational models: property testing and data streaming. We present a novel framework closely linking these areas in the setting of general graphs in the context of constant-query complexity testing and constant-space streaming. Our main result is a generic transformation of a one-sided error property tester in the random-neighbor model with constant query complexity into a one-sided error property tester in the streaming model with constant space complexity. Previously such a generic transformation was only known for bounded-degree graphs.
Cite as

Artur Czumaj, Hendrik Fichtenberger, Pan Peng, and Christian Sohler. Testable Properties in General Graphs and Random Order Streaming. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{czumaj_et_al:LIPIcs.APPROX/RANDOM.2020.16,
  author =	{Czumaj, Artur and Fichtenberger, Hendrik and Peng, Pan and Sohler, Christian},
  title =	{{Testable Properties in General Graphs and Random Order Streaming}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{16:1--16:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.16},
  URN =		{urn:nbn:de:0030-drops-126190},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.16},
  annote =	{Keywords: Graph property testing, sublinear algorithms, graph streaming algorithms}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.ESA.2017
LIPIcs, Volume 87, ESA'17, Complete Volume

Authors: Kirk Pruhs and Christian Sohler

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
LIPIcs, Volume 87, ESA'17, Complete Volume
Cite as

25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@Proceedings{pruhs_et_al:LIPIcs.ESA.2017,
  title =	{{LIPIcs, Volume 87, ESA'17, Complete Volume}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017},
  URN =		{urn:nbn:de:0030-drops-79096},
  doi =		{10.4230/LIPIcs.ESA.2017},
  annote =	{Keywords: Data Structures, Nonnumerical Algorithms and Problems, Optimization, Discrete Mathematics, Mathematical Software, AlgorithmsProblem Solving, Control Methods, and Search, Computational Geometry and Object Modeling}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.ESA.2017.0
Front Matter, Table of Contents, Preface, Programm Commitees, External Reviewers

Authors: Kirk Pruhs and Christian Sohler

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
Front Matter, Table of Contents, Preface, Programm Commitees, External Reviewers
Cite as

25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 0:i-0:xx, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{pruhs_et_al:LIPIcs.ESA.2017.0,
  author =	{Pruhs, Kirk and Sohler, Christian},
  title =	{{Front Matter, Table of Contents, Preface, Programm Commitees, External Reviewers}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{0:i--0:xx},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.0},
  URN =		{urn:nbn:de:0030-drops-78147},
  doi =		{10.4230/LIPIcs.ESA.2017.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Programm Commitees, External Reviewers}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ESA.2017.1
Sketching for Geometric Problems (Invited Talk)

Authors: David P. Woodruff

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
In this invited talk at the European Symposium on Algorithms (ESA), 2017, I will discuss a tool called sketching, which is a form of data dimensionality reduction, and its applications to several problems in high dimensional geometry. In particular, I will show how to obtain the fastest possible algorithms for fundamental problems such as projection onto a flat, and also study generalizations of projection onto more complicated objects such as the union of flats or subspaces. Some of these problems are just least squares regression problems, with many applications in machine learning, numerical linear algebra, and optimization. I will also discuss low rank approximation, with applications to clustering. Finally I will mention a number of other applications of sketching in machine learning, numerical linear algebra, and optimization.
Cite as

David P. Woodruff. Sketching for Geometric Problems (Invited Talk). In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 1:1-1:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{woodruff:LIPIcs.ESA.2017.1,
  author =	{Woodruff, David P.},
  title =	{{Sketching for Geometric Problems}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{1:1--1:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.1},
  URN =		{urn:nbn:de:0030-drops-78848},
  doi =		{10.4230/LIPIcs.ESA.2017.1},
  annote =	{Keywords: dimensionality reduction, low rank approximation, projection, regression, sketching}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.2
Permuting and Batched Geometric Lower Bounds in the I/O Model

Authors: Peyman Afshani and Ingo van Duijn

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
We study permuting and batched orthogonal geometric reporting problems in the External Memory Model (EM), assuming indivisibility of the input records. Our main results are twofold. First, we prove a general simulation result that essentially shows that any permutation algorithm (resp. duplicate removal algorithm) that does alpha*N/B I/Os (resp. to remove a fraction of the existing duplicates) can be simulated with an algorithm that does alpha phases where each phase reads and writes each element once, but using a factor alpha smaller block size. Second, we prove two lower bounds for batched rectangle stabbing and batched orthogonal range reporting queries. Assuming a short cache, we prove very high lower bounds that currently are not possible with the existing techniques under the tall cache assumption.
Cite as

Peyman Afshani and Ingo van Duijn. Permuting and Batched Geometric Lower Bounds in the I/O Model. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 2:1-2:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{afshani_et_al:LIPIcs.ESA.2017.2,
  author =	{Afshani, Peyman and van Duijn, Ingo},
  title =	{{Permuting and Batched Geometric Lower Bounds in the I/O Model}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{2:1--2:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.2},
  URN =		{urn:nbn:de:0030-drops-78695},
  doi =		{10.4230/LIPIcs.ESA.2017.2},
  annote =	{Keywords: I/O Model, Batched Geometric Queries, Lower Bounds, Permuting}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.3
Independent Range Sampling, Revisited

Authors: Peyman Afshani and Zhewei Wei

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
In the independent range sampling (IRS) problem, given an input set P of n points in R^d, the task is to build a data structure, such that given a range R and an integer t >= 1, it returns t points that are uniformly and independently drawn from P cap R. The samples must satisfy inter-query independence, that is, the samples returned by every query must be independent of the samples returned by all the previous queries. This problem was first tackled by Hu, Qiao and Tao in 2014, who proposed optimal structures for one-dimensional dynamic IRS problem in internal memory and one-dimensional static IRS problem in external memory. In this paper, we study two natural extensions of the independent range sampling problem. In the first extension, we consider the static IRS problem in two and three dimensions in internal memory. We obtain data structures with optimal space-query tradeoffs for 3D halfspace, 3D dominance, and 2D three-sided queries. The second extension considers weighted IRS problem. Each point is associated with a real-valued weight, and given a query range R, a sample is drawn independently such that each point in P cap R is selected with probability proportional to its weight. Walker's alias method is a classic solution to this problem when no query range is specified. We obtain optimal data structure for one dimensional weighted range sampling problem, thereby extending the alias method to allow range queries.
Cite as

Peyman Afshani and Zhewei Wei. Independent Range Sampling, Revisited. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 3:1-3:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{afshani_et_al:LIPIcs.ESA.2017.3,
  author =	{Afshani, Peyman and Wei, Zhewei},
  title =	{{Independent Range Sampling, Revisited}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{3:1--3:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.3},
  URN =		{urn:nbn:de:0030-drops-78592},
  doi =		{10.4230/LIPIcs.ESA.2017.3},
  annote =	{Keywords: data structures, range searching, range sampling, random sampling}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.4
Approximate Nearest Neighbor Search Amid Higher-Dimensional Flats

Authors: Pankaj K. Agarwal, Natan Rubin, and Micha Sharir

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
We consider the Approximate Nearest Neighbor (ANN) problem where the input set consists of n k-flats in the Euclidean Rd, for any fixed parameters k<d, and where, for each query point q, we want to return an input flat whose distance from q is at most (1 + epsilon) times the shortest such distance, where epsilon > 0 is another prespecified parameter. We present an algorithm that achieves this task with n^{k+1}(log(n)/epsilon)^O(1) storage and preprocessing (where the constant of proportionality in the big-O notation depends on d), and can answer a query in O(polylog(n)) time (where the power of the logarithm depends on d and k). In particular, we need only near-quadratic storage to answer ANN queries amidst a set of n lines in any fixed-dimensional Euclidean space. As a by-product, our approach also yields an algorithm, with similar performance bounds, for answering exact nearest neighbor queries amidst k-flats with respect to any polyhedral distance function. Our results are more general, in that they also provide a tradeoff between storage and query time.
Cite as

Pankaj K. Agarwal, Natan Rubin, and Micha Sharir. Approximate Nearest Neighbor Search Amid Higher-Dimensional Flats. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 4:1-4:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{agarwal_et_al:LIPIcs.ESA.2017.4,
  author =	{Agarwal, Pankaj K. and Rubin, Natan and Sharir, Micha},
  title =	{{Approximate Nearest Neighbor Search Amid Higher-Dimensional Flats}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{4:1--4:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.4},
  URN =		{urn:nbn:de:0030-drops-78182},
  doi =		{10.4230/LIPIcs.ESA.2017.4},
  annote =	{Keywords: Approximate nearest neighbor search, k-flats, Polyhedral distance functions, Linear programming queries}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.5
Output Sensitive Algorithms for Approximate Incidences and Their Applications

Authors: Dror Aiger, Haim Kaplan, and Micha Sharir

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
An epsilon-approximate incidence between a point and some geometric object (line, circle, plane, sphere) occurs when the point and the object lie at distance at most epsilon from each other. Given a set of points and a set of objects, computing the approximate incidences between them is a major step in many database and web-based applications in computer vision and graphics, including robust model fitting, approximate point pattern matching, and estimating the fundamental matrix in epipolar (stereo) geometry. In a typical approximate incidence problem of this sort, we are given a set P of m points in two or three dimensions, a set S of n objects (lines, circles, planes, spheres), and an error parameter epsilon>0, and our goal is to report all pairs (p,s) in P times S that lie at distance at most epsilon from one another. We present efficient output-sensitive approximation algorithms for quite a few cases, including points and lines or circles in the plane, and points and planes, spheres, lines, or circles in three dimensions. Several of these cases arise in the applications mentioned above. Our algorithms report all pairs at distance <= epsilon, but may also report additional pairs, all of which are guaranteed to be at distance at most alphaepsilon, for some constant alpha>1. Our algorithms are based on simple primal and dual grid decompositions and are easy to implement. We note though that (a) the use of duality, which leads to significant improvements in the overhead cost of the algorithms, appears to be novel for this kind of problems; (b) the correct choice of duality in some of these problems is fairly intricate and requires some care; and (c) the correctness and performance analysis of the algorithms (especially in the more advanced versions) is fairly non-trivial. We analyze our algorithms and prove guaranteed upper bounds on their running time and on the "distortion" parameter alpha. We also briefly describe the motivating applications, and show how they can effectively exploit our solutions. The superior theoretical bounds on the performance of our algorithms, and their simplicity, make them indeed ideal tools for these applications. In a series of preliminary experimentations (not included in this abstract), we substantiate this feeling, and show that our algorithms lead in practice to significant improved performance of the aforementioned applications.
Cite as

Dror Aiger, Haim Kaplan, and Micha Sharir. Output Sensitive Algorithms for Approximate Incidences and Their Applications. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 5:1-5:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{aiger_et_al:LIPIcs.ESA.2017.5,
  author =	{Aiger, Dror and Kaplan, Haim and Sharir, Micha},
  title =	{{Output Sensitive Algorithms for Approximate Incidences and Their Applications}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{5:1--5:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.5},
  URN =		{urn:nbn:de:0030-drops-78224},
  doi =		{10.4230/LIPIcs.ESA.2017.5},
  annote =	{Keywords: Approximate incidences, near-neighbor reporting, duality, grid-based approximation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.6
Randomized Contractions for Multiobjective Minimum Cuts

Authors: Hassene Aissi, Ali Ridha Mahjoub, and R. Ravi

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
We show that Karger's randomized contraction method (SODA 93) can be adapted to multiobjective global minimum cut problems with a constant number of edge or node budget constraints to give efficient algorithms. For global minimum cuts with a single edge-budget constraint, our extension of the randomized contraction method has running time tilde{O}(n^3) in an n-node graph improving upon the best-known randomized algorithm with running time tilde{O}(n^4) due to Armon and Zwick (Algorithmica 2006). Our analysis also gives a new upper bound of O(n^3) for the number of optimal solutions for a single edge-budget min cut problem. For the case of (k-1) edge-budget constraints, the extension of our algorithm saves a logarithmic factor from the best-known randomized running time of O(n^{2k} log^3 n). A main feature of our algorithms is to adaptively choose, at each step, the appropriate cost function used in the random selection of edges to be contracted. For the global min cut problem with a constant number of node budgets, we give a randomized algorithm with running time tilde{O}(n^2), improving the current best determinisitic running time of O(n^3) due to Goemans and Soto (SIAM Journal on Discrete Mathematics 2013). Our method also shows that the total number of distinct optimal solutions is bounded by O(n^2) as in the case of global min-cuts. Our algorithm extends to the node-budget constrained global min cut problem excluding a given sink with the same running time and bound on number of optimal solutions, again improving upon the best-known running time by a factor of O(n). For node-budget constrained problems, our improvements arise from incorporating the idea of merging any infeasible super-nodes that arise during the random contraction process. In contrast to cuts excluding a sink, we note that the node-cardinality constrained min-cut problem containing a given source is strongly NP-hard using a reduction from graph bisection.
Cite as

Hassene Aissi, Ali Ridha Mahjoub, and R. Ravi. Randomized Contractions for Multiobjective Minimum Cuts. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{aissi_et_al:LIPIcs.ESA.2017.6,
  author =	{Aissi, Hassene and Mahjoub, Ali Ridha and Ravi, R.},
  title =	{{Randomized Contractions for Multiobjective Minimum Cuts}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{6:1--6:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.6},
  URN =		{urn:nbn:de:0030-drops-78686},
  doi =		{10.4230/LIPIcs.ESA.2017.6},
  annote =	{Keywords: minimum cut, multiobjective optimization, budget constraints, graph algorithms, randomized algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.7
Tight Bounds for Online Coloring of Basic Graph Classes

Authors: Susanne Albers and Sebastian Schraink

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
We resolve a number of long-standing open problems in online graph coloring. More specifically, we develop tight lower bounds on the performance of online algorithms for fundamental graph classes. An important contribution is that our bounds also hold for randomized online algorithms, for which hardly any results were known. Technically, we construct lower bounds for chordal graphs. The constructions then allow us to derive results on the performance of randomized online algorithms for the following further graph classes: trees, planar, bipartite, inductive, bounded-treewidth and disk graphs. It shows that the best competitive ratio of both deterministic and randomized online algorithms is Theta(log n), where n is the number of vertices of a graph. Furthermore, we prove that this guarantee cannot be improved if an online algorithm has a lookahead of size O(n/log n) or access to a reordering buffer of size n^(1-epsilon), for any 0 < epsilon <= 1. A consequence of our results is that, for all of the above mentioned graph classes except bipartite graphs, the natural First Fit coloring algorithm achieves an optimal performance, up to constant factors, among deterministic and randomized online algorithms.
Cite as

Susanne Albers and Sebastian Schraink. Tight Bounds for Online Coloring of Basic Graph Classes. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{albers_et_al:LIPIcs.ESA.2017.7,
  author =	{Albers, Susanne and Schraink, Sebastian},
  title =	{{Tight Bounds for Online Coloring of Basic Graph Classes}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{7:1--7:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.7},
  URN =		{urn:nbn:de:0030-drops-78268},
  doi =		{10.4230/LIPIcs.ESA.2017.7},
  annote =	{Keywords: graph coloring, online algorithms, lower bounds, randomization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.8
Combinatorics of Local Search: An Optimal 4-Local Hall's Theorem for Planar Graphs

Authors: Daniel Antunes, Claire Mathieu, and Nabil H. Mustafa

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
Local search for combinatorial optimization problems is becoming a dominant algorithmic paradigm, with several papers using it to resolve long-standing open problems. In this paper, we prove the following `4-local' version of Hall's theorem for planar graphs: given a bipartite planar graph G = (B, R, E) such that |N(B')| >= |B'| for all |B'| <= 4, there exists a matching of size at least |B|/4 in G; furthermore this bound is tight. Besides immediately implying improved bounds for several problems studied in previous papers, we find this variant of Hall's theorem to be of independent interest in graph theory.
Cite as

Daniel Antunes, Claire Mathieu, and Nabil H. Mustafa. Combinatorics of Local Search: An Optimal 4-Local Hall's Theorem for Planar Graphs. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{antunes_et_al:LIPIcs.ESA.2017.8,
  author =	{Antunes, Daniel and Mathieu, Claire and Mustafa, Nabil H.},
  title =	{{Combinatorics of Local Search: An Optimal 4-Local Hall's Theorem for Planar Graphs}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{8:1--8:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.8},
  URN =		{urn:nbn:de:0030-drops-78293},
  doi =		{10.4230/LIPIcs.ESA.2017.8},
  annote =	{Keywords: Planar graphs, Local search, Hall's theorem, Combinatorial optimization, Expansion}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.9
In-Place Parallel Super Scalar Samplesort (IPSSSSo)

Authors: Michael Axtmann, Sascha Witt, Daniel Ferizovic, and Peter Sanders

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
We present a sorting algorithm that works in-place, executes in parallel, is cache-efficient, avoids branch-mispredictions, and performs work O(n log n) for arbitrary inputs with high probability. The main algorithmic contributions are new ways to make distribution-based algorithms in-place: On the practical side, by using coarse-grained block-based permutations, and on the theoretical side, we show how to eliminate the recursion stack. Extensive experiments shw that our algorithm IPSSSSo scales well on a variety of multi-core machines. We outperform our closest in-place competitor by a factor of up to 3. Even as a sequential algorithm, we are up to 1.5 times faster than the closest sequential competitor, BlockQuicksort.
Cite as

Michael Axtmann, Sascha Witt, Daniel Ferizovic, and Peter Sanders. In-Place Parallel Super Scalar Samplesort (IPSSSSo). In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{axtmann_et_al:LIPIcs.ESA.2017.9,
  author =	{Axtmann, Michael and Witt, Sascha and Ferizovic, Daniel and Sanders, Peter},
  title =	{{In-Place Parallel Super Scalar Samplesort (IPSSSSo)}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.9},
  URN =		{urn:nbn:de:0030-drops-78542},
  doi =		{10.4230/LIPIcs.ESA.2017.9},
  annote =	{Keywords: shared memory, parallel sorting, in-place algorithm, comparison-based sorting, branch prediction}
}
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