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Volume

LIPIcs, Volume 112

26th Annual European Symposium on Algorithms (ESA 2018)

ESA 2018, August 20-22, 2018, Helsinki, Finland

Editors: Yossi Azar, Hannah Bast, and Grzegorz Herman

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2023.13

Multi Layer Peeling for Linear Arrangement and Hierarchical Clustering

Authors: Yossi Azar and Danny Vainstein

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

Abstract

We present a new multi-layer peeling technique to cluster points in a metric space. A well-known non-parametric objective is to embed the metric space into a simpler structured metric space such as a line (i.e., Linear Arrangement) or a binary tree (i.e., Hierarchical Clustering). Points which are close in the metric space should be mapped to close points/leaves in the line/tree; similarly, points which are far in the metric space should be far in the line or on the tree. In particular we consider the Maximum Linear Arrangement problem [Refael Hassin and Shlomi Rubinstein, 2001] and the Maximum Hierarchical Clustering problem [Vincent Cohen-Addad et al., 2018] applied to metrics. We design approximation schemes (1-ε approximation for any constant ε > 0) for these objectives. In particular this shows that by considering metrics one may significantly improve former approximations (0.5 for Max Linear Arrangement and 0.74 for Max Hierarchical Clustering). Our main technique, which is called multi-layer peeling, consists of recursively peeling off points which are far from the "core" of the metric space. The recursion ends once the core becomes a sufficiently densely weighted metric space (i.e. the average distance is at least a constant times the diameter) or once it becomes negligible with respect to its inner contribution to the objective. Interestingly, the algorithm in the Linear Arrangement case is much more involved than that in the Hierarchical Clustering case, and uses a significantly more delicate peeling.

Cite as

Yossi Azar and Danny Vainstein. Multi Layer Peeling for Linear Arrangement and Hierarchical Clustering. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 13:1-13:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{azar_et_al:LIPIcs.ICALP.2023.13,
  author =	{Azar, Yossi and Vainstein, Danny},
  title =	{{Multi Layer Peeling for Linear Arrangement and Hierarchical Clustering}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{13:1--13:18},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.13},
  URN =		{urn:nbn:de:0030-drops-180656},
  doi =		{10.4230/LIPIcs.ICALP.2023.13},
  annote =	{Keywords: Hierarchical clustering, Linear arrangements, Metric embeddings}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2022.16

Distortion-Oblivious Algorithms for Scheduling on Multiple Machines

Authors: Yossi Azar, Eldad Peretz, and Noam Touitou

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract

We consider the classic online problem of scheduling on multiple machines to minimize total flow time and total stretch where the input consists of estimates on the processing time provided for each job once released. The performance of such algorithms should depend on μ, the error in the estimates of the processing time for that instance (such an algorithm is called a distortion oblivious algorithm). Previously, a distortion oblivious algorithm to minimize flow time was provided only for a single machine. In this paper we extend the work to multiple machines and also consider the total stretch objective. In particular, we design a non-migrative distortion oblivious algorithm to minimize total flow time with a competitive ratio of O(μ log P), where P is the ratio between the maximum to minimum processing time. We show that with immediate-dispatching one cannot achieve a competitive ratio which is a function of μ and P; moreover, a competitive ratio which is sub-polynomial in the number of jobs is also impossible. We also present the first distortion-oblivious algorithm for minimizing the stretch time, both on a single and on multiple machines. The competitive ratio of these algorithms are O(μ²) which is optimal as we also prove a matching Ω(μ²) lower bound.

Cite as

Yossi Azar, Eldad Peretz, and Noam Touitou. Distortion-Oblivious Algorithms for Scheduling on Multiple Machines. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 16:1-16:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{azar_et_al:LIPIcs.ISAAC.2022.16,
  author =	{Azar, Yossi and Peretz, Eldad and Touitou, Noam},
  title =	{{Distortion-Oblivious Algorithms for Scheduling on Multiple Machines}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.16},
  URN =		{urn:nbn:de:0030-drops-173010},
  doi =		{10.4230/LIPIcs.ISAAC.2022.16},
  annote =	{Keywords: Online, Scheduling, Predictions, Stretch, Flow Time}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2022.13

Competitive Vertex Recoloring

Authors: Yossi Azar, Chay Machluf, Boaz Patt-Shamir, and Noam Touitou

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract

Motivated by placement of jobs in physical machines, we introduce and analyze the problem of online recoloring, or online disengagement. In this problem, we are given a set of n weighted vertices and a k-coloring of the vertices (vertices represent jobs, and colors represent physical machines). Edges, representing conflicts between jobs, are inserted in an online fashion. After every edge insertion, the algorithm must output a proper k-coloring of the vertices. The cost of a recoloring is the sum of weights of vertices whose color changed. Our aim is to minimize the competitive ratio of the algorithm, i.e., the ratio between the cost paid by the online algorithm and the cost paid by an optimal, offline algorithm. We consider a couple of polynomially-solvable coloring variants. Specifically, for 2-coloring bipartite graphs we present an O(log n)-competitive deterministic algorithm and an Ω(log n) lower bound on the competitive ratio of randomized algorithms. For (Δ+1)-coloring, we present tight bounds of Θ(Δ) and Θ(logΔ) on the competitive ratios of deterministic and randomized algorithms, respectively (where Δ denotes the maximum degree). We also consider a dynamic case which allows edge deletions as well as insertions. All our algorithms are applicable to the case where vertices are weighted and the cost of recoloring a vertex is its weight. All our lower bounds hold even in the unweighted case.

Cite as

Yossi Azar, Chay Machluf, Boaz Patt-Shamir, and Noam Touitou. Competitive Vertex Recoloring. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 13:1-13:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{azar_et_al:LIPIcs.ICALP.2022.13,
  author =	{Azar, Yossi and Machluf, Chay and Patt-Shamir, Boaz and Touitou, Noam},
  title =	{{Competitive Vertex Recoloring}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{13:1--13:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.13},
  URN =		{urn:nbn:de:0030-drops-163542},
  doi =		{10.4230/LIPIcs.ICALP.2022.13},
  annote =	{Keywords: coloring with recourse, anti-affinity constraints}
}

Document

DOI: 10.4230/LIPIcs.ESA.2020.8

Set Cover with Delay - Clairvoyance Is Not Required

Authors: Yossi Azar, Ashish Chiplunkar, Shay Kutten, and Noam Touitou

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract

In most online problems with delay, clairvoyance (i.e. knowing the future delay of a request upon its arrival) is required for polylogarithmic competitiveness. In this paper, we show that this is not the case for set cover with delay (SCD) - specifically, we present the first non-clairvoyant algorithm, which is O(log n log m)-competitive, where n is the number of elements and m is the number of sets. This matches the best known result for the classic online set cover (a special case of non-clairvoyant SCD). Moreover, clairvoyance does not allow for significant improvement - we present lower bounds of Ω(√{log n}) and Ω(√{log m}) for SCD which apply for the clairvoyant case. In addition, the competitiveness of our algorithm does not depend on the number of requests. Such a guarantee on the size of the universe alone was not previously known even for the clairvoyant case - the only previously-known algorithm (due to Carrasco et al.) is clairvoyant, with competitiveness that grows with the number of requests. For the special case of vertex cover with delay, we show a simpler, deterministic algorithm which is 3-competitive (and also non-clairvoyant).

Cite as

Yossi Azar, Ashish Chiplunkar, Shay Kutten, and Noam Touitou. Set Cover with Delay - Clairvoyance Is Not Required. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 8:1-8:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{azar_et_al:LIPIcs.ESA.2020.8,
  author =	{Azar, Yossi and Chiplunkar, Ashish and Kutten, Shay and Touitou, Noam},
  title =	{{Set Cover with Delay - Clairvoyance Is Not Required}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{8:1--8:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.8},
  URN =		{urn:nbn:de:0030-drops-128749},
  doi =		{10.4230/LIPIcs.ESA.2020.8},
  annote =	{Keywords: Set Cover, Delay, Clairvoyant}
}

Document

Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management

DOI: 10.4230/LIPIcs.ICALP.2019.136

Stochastic Graph Exploration

Authors: Aris Anagnostopoulos, Ilan R. Cohen, Stefano Leonardi, and Jakub Łącki

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract

Exploring large-scale networks is a time consuming and expensive task which is usually operated in a complex and uncertain environment. A crucial aspect of network exploration is the development of suitable strategies that decide which nodes and edges to probe at each stage of the process. To model this process, we introduce the stochastic graph exploration problem. The input is an undirected graph G=(V,E) with a source vertex s, stochastic edge costs drawn from a distribution pi_e, e in E, and rewards on vertices of maximum value R. The goal is to find a set F of edges of total cost at most B such that the subgraph of G induced by F is connected, contains s, and maximizes the total reward. This problem generalizes the stochastic knapsack problem and other stochastic probing problems recently studied. Our focus is on the development of efficient nonadaptive strategies that are competitive against the optimal adaptive strategy. A major challenge is the fact that the problem has an Omega(n) adaptivity gap even on a tree of n vertices. This is in sharp contrast with O(1) adaptivity gap of the stochastic knapsack problem, which is a special case of our problem. We circumvent this negative result by showing that O(log nR) resource augmentation suffices to obtain O(1) approximation on trees and O(log nR) approximation on general graphs. To achieve this result, we reduce stochastic graph exploration to a memoryless process - the minesweeper problem - which assigns to every edge a probability that the process terminates when the edge is probed. For this problem, interesting in its own, we present an optimal polynomial time algorithm on trees and an O(log nR) approximation for general graphs. We study also the problem in which the maximum cost of an edge is a logarithmic fraction of the budget. We show that under this condition, there exist polynomial-time oblivious strategies that use 1+epsilon budget, whose adaptivity gaps on trees and general graphs are 1+epsilon and 8+epsilon, respectively. Finally, we provide additional results on the structure and the complexity of nonadaptive and adaptive strategies.

Cite as

Aris Anagnostopoulos, Ilan R. Cohen, Stefano Leonardi, and Jakub Łącki. Stochastic Graph Exploration. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 136:1-136:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{anagnostopoulos_et_al:LIPIcs.ICALP.2019.136,
  author =	{Anagnostopoulos, Aris and Cohen, Ilan R. and Leonardi, Stefano and {\L}\k{a}cki, Jakub},
  title =	{{Stochastic Graph Exploration}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{136:1--136:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.136},
  URN =		{urn:nbn:de:0030-drops-107122},
  doi =		{10.4230/LIPIcs.ICALP.2019.136},
  annote =	{Keywords: stochastic optimization, graph exploration, approximation algorithms}
}

Document

Complete Volume

DOI: 10.4230/LIPIcs.ESA.2018

LIPIcs, Volume 112, ESA'18, Complete Volume

Authors: Yossi Azar, Hannah Bast, and Grzegorz Herman

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract

LIPIcs, Volume 112, ESA'18, Complete Volume

Cite as

Yossi Azar, Hannah Bast, and Grzegorz Herman. LIPIcs, Volume 112, ESA'18, Complete Volume. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@Proceedings{azar_et_al:LIPIcs.ESA.2018,
  title =	{{LIPIcs, Volume 112, ESA'18, Complete Volume}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018},
  URN =		{urn:nbn:de:0030-drops-97239},
  doi =		{10.4230/LIPIcs.ESA.2018},
  annote =	{Keywords: Computer systems organization, Single instruction, multiple data, Computing methodologies, Graphics processors, Robotic planning, Hardware}
}

Document

Front Matter

DOI: 10.4230/LIPIcs.ESA.2018.0

Front Matter, Table of Contents, Preface, Conference Organization

Authors: Yossi Azar, Hannah Bast, and Grzegorz Herman

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract

Front Matter, Table of Contents, Preface, Conference Organization

Cite as

Yossi Azar, Hannah Bast, and Grzegorz Herman. Front Matter, Table of Contents, Preface, Conference Organization. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 0:i-0:xx, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{azar_et_al:LIPIcs.ESA.2018.0,
  author =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{0:i--0:xx},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.0},
  URN =		{urn:nbn:de:0030-drops-94631},
  doi =		{10.4230/LIPIcs.ESA.2018.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}

Document

DOI: 10.4230/LIPIcs.ESA.2018.1

Algorithms for Inverse Optimization Problems

Authors: Sara Ahmadian, Umang Bhaskar, Laura Sanità, and Chaitanya Swamy

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract

We study inverse optimization problems, wherein the goal is to map given solutions to an underlying optimization problem to a cost vector for which the given solutions are the (unique) optimal solutions. Inverse optimization problems find diverse applications and have been widely studied. A prominent problem in this field is the inverse shortest path (ISP) problem [D. Burton and Ph.L. Toint, 1992; W. Ben-Ameur and E. Gourdin, 2004; A. Bley, 2007], which finds applications in shortest-path routing protocols used in telecommunications. Here we seek a cost vector that is positive, integral, induces a set of given paths as the unique shortest paths, and has minimum l_infty norm. Despite being extensively studied, very few algorithmic results are known for inverse optimization problems involving integrality constraints on the desired cost vector whose norm has to be minimized. Motivated by ISP, we initiate a systematic study of such integral inverse optimization problems from the perspective of designing polynomial time approximation algorithms. For ISP, our main result is an additive 1-approximation algorithm for multicommodity ISP with node-disjoint commodities, which we show is tight assuming P!=NP. We then consider the integral-cost inverse versions of various other fundamental combinatorial optimization problems, including min-cost flow, max/min-cost bipartite matching, and max/min-cost basis in a matroid, and obtain tight or nearly-tight approximation guarantees for these. Our guarantees for the first two problems are based on results for a broad generalization, namely integral inverse polyhedral optimization, for which we also give approximation guarantees. Our techniques also give similar results for variants, including l_p-norm minimization of the integral cost vector, and distance-minimization from an initial cost vector.

Cite as

Sara Ahmadian, Umang Bhaskar, Laura Sanità, and Chaitanya Swamy. Algorithms for Inverse Optimization Problems. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 1:1-1:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ahmadian_et_al:LIPIcs.ESA.2018.1,
  author =	{Ahmadian, Sara and Bhaskar, Umang and Sanit\`{a}, Laura and Swamy, Chaitanya},
  title =	{{Algorithms for Inverse Optimization Problems}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{1:1--1:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.1},
  URN =		{urn:nbn:de:0030-drops-94646},
  doi =		{10.4230/LIPIcs.ESA.2018.1},
  annote =	{Keywords: Inverse optimization, Shortest paths, Approximation algorithms, Linear programming, Polyhedral theory, Combinatorial optimization}
}

Document

DOI: 10.4230/LIPIcs.ESA.2018.2

Two-Dimensional Maximal Repetitions

Authors: Amihood Amir, Gad M. Landau, Shoshana Marcus, and Dina Sokol

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract

Maximal repetitions or runs in strings have a wide array of applications and thus have been extensively studied. In this paper, we extend this notion to 2-dimensions, precisely defining a maximal 2D repetition. We provide initial bounds on the number of maximal 2D repetitions that can occur in a matrix. The main contribution of this paper is the presentation of the first algorithm for locating all maximal 2D repetitions in a matrix. The algorithm is efficient and straightforward, with runtime O(n^2 log n log log n+ rho log n), where n^2 is the size of the input, and rho is the number of 2D repetitions in the output.

Cite as

Amihood Amir, Gad M. Landau, Shoshana Marcus, and Dina Sokol. Two-Dimensional Maximal Repetitions. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 2:1-2:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{amir_et_al:LIPIcs.ESA.2018.2,
  author =	{Amir, Amihood and Landau, Gad M. and Marcus, Shoshana and Sokol, Dina},
  title =	{{Two-Dimensional Maximal Repetitions}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{2:1--2:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.2},
  URN =		{urn:nbn:de:0030-drops-94652},
  doi =		{10.4230/LIPIcs.ESA.2018.2},
  annote =	{Keywords: pattern matching algorithms, repetitions, periodicity, two-dimensional}
}

Document

DOI: 10.4230/LIPIcs.ESA.2018.3

Approximate Convex Intersection Detection with Applications to Width and Minkowski Sums

Authors: Sunil Arya, Guilherme D. da Fonseca, and David M. Mount

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract

Approximation problems involving a single convex body in R^d have received a great deal of attention in the computational geometry community. In contrast, works involving multiple convex bodies are generally limited to dimensions d <= 3 and/or do not consider approximation. In this paper, we consider approximations to two natural problems involving multiple convex bodies: detecting whether two polytopes intersect and computing their Minkowski sum. Given an approximation parameter epsilon > 0, we show how to independently preprocess two polytopes A,B subset R^d into data structures of size O(1/epsilon^{(d-1)/2}) such that we can answer in polylogarithmic time whether A and B intersect approximately. More generally, we can answer this for the images of A and B under affine transformations. Next, we show how to epsilon-approximate the Minkowski sum of two given polytopes defined as the intersection of n halfspaces in O(n log(1/epsilon) + 1/epsilon^{(d-1)/2 + alpha}) time, for any constant alpha > 0. Finally, we present a surprising impact of these results to a well studied problem that considers a single convex body. We show how to epsilon-approximate the width of a set of n points in O(n log(1/epsilon) + 1/epsilon^{(d-1)/2 + alpha}) time, for any constant alpha > 0, a major improvement over the previous bound of roughly O(n + 1/epsilon^{d-1}) time.

Cite as

Sunil Arya, Guilherme D. da Fonseca, and David M. Mount. Approximate Convex Intersection Detection with Applications to Width and Minkowski Sums. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 3:1-3:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{arya_et_al:LIPIcs.ESA.2018.3,
  author =	{Arya, Sunil and da Fonseca, Guilherme D. and Mount, David M.},
  title =	{{Approximate Convex Intersection Detection with Applications to Width and Minkowski Sums}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{3:1--3:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.3},
  URN =		{urn:nbn:de:0030-drops-94664},
  doi =		{10.4230/LIPIcs.ESA.2018.3},
  annote =	{Keywords: Minkowski sum, convex intersection, width, approximation}
}

Document

DOI: 10.4230/LIPIcs.ESA.2018.4

On the Worst-Case Complexity of TimSort

Authors: Nicolas Auger, Vincent Jugé, Cyril Nicaud, and Carine Pivoteau

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract

TimSort is an intriguing sorting algorithm designed in 2002 for Python, whose worst-case complexity was announced, but not proved until our recent preprint. In fact, there are two slightly different versions of TimSort that are currently implemented in Python and in Java respectively. We propose a pedagogical and insightful proof that the Python version runs in O(n log n). The approach we use in the analysis also applies to the Java version, although not without very involved technical details. As a byproduct of our study, we uncover a bug in the Java implementation that can cause the sorting method to fail during the execution. We also give a proof that Python's TimSort running time is in O(n + n log rho), where rho is the number of runs (i.e. maximal monotonic sequences), which is quite a natural parameter here and part of the explanation for the good behavior of TimSort on partially sorted inputs.

Cite as

Nicolas Auger, Vincent Jugé, Cyril Nicaud, and Carine Pivoteau. On the Worst-Case Complexity of TimSort. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 4:1-4:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{auger_et_al:LIPIcs.ESA.2018.4,
  author =	{Auger, Nicolas and Jug\'{e}, Vincent and Nicaud, Cyril and Pivoteau, Carine},
  title =	{{On the Worst-Case Complexity of TimSort}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{4:1--4:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.4},
  URN =		{urn:nbn:de:0030-drops-94678},
  doi =		{10.4230/LIPIcs.ESA.2018.4},
  annote =	{Keywords: Sorting algorithms, Merge sorting algorithms, TimSort, Analysis of algorithms}
}

Document

DOI: 10.4230/LIPIcs.ESA.2018.5

A New and Improved Algorithm for Online Bin Packing

Authors: János Balogh, József Békési, György Dósa, Leah Epstein, and Asaf Levin

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract

We revisit the classic online bin packing problem studied in the half-century. In this problem, items of positive sizes no larger than 1 are presented one by one to be packed into subsets called bins of total sizes no larger than 1, such that every item is assigned to a bin before the next item is presented. We use online partitioning of items into classes based on sizes, as in previous work, but we also apply a new method where items of one class can be packed into more than two types of bins, where a bin type is defined according to the number of such items grouped together. Additionally, we allow the smallest class of items to be packed in multiple kinds of bins, and not only into their own bins. We combine this with the approach of packing of sufficiently big items according to their exact sizes. Finally, we simplify the analysis of such algorithms, allowing the analysis to be based on the most standard weight functions. This simplified analysis allows us to study the algorithm which we defined based on all these ideas. This leads us to the design and analysis of the first algorithm of asymptotic competitive ratio strictly below 1.58, specifically, we break this barrier by providing an algorithm AH (Advanced Harmonic) whose asymptotic competitive ratio does not exceed 1.57829. Our main contribution is the introduction of the simple analysis based on weight function to analyze the state of the art online algorithms for the classic online bin packing problem. The previously used analytic tool named weight system was too complicated for the community in this area to adjust it for other problems and other algorithmic tools that are needed in order to improve the current best algorithms. We show that the weight system based analysis is not needed for the analysis of the current algorithms for the classic online bin packing problem. The importance of a simple analysis is demonstrated by analyzing several new features together with all existing techniques, and by proving a better competitive ratio than the previously best one.

Cite as

János Balogh, József Békési, György Dósa, Leah Epstein, and Asaf Levin. A New and Improved Algorithm for Online Bin Packing. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 5:1-5:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{balogh_et_al:LIPIcs.ESA.2018.5,
  author =	{Balogh, J\'{a}nos and B\'{e}k\'{e}si, J\'{o}zsef and D\'{o}sa, Gy\"{o}rgy and Epstein, Leah and Levin, Asaf},
  title =	{{A New and Improved Algorithm for Online Bin Packing}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{5:1--5:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.5},
  URN =		{urn:nbn:de:0030-drops-94686},
  doi =		{10.4230/LIPIcs.ESA.2018.5},
  annote =	{Keywords: Bin packing, online algorithms, competitive analysis}
}

Document

DOI: 10.4230/LIPIcs.ESA.2018.6

Practical Access to Dynamic Programming on Tree Decompositions

Authors: Max Bannach and Sebastian Berndt

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract

Parameterized complexity theory has lead to a wide range of algorithmic breakthroughs within the last decades, but the practicability of these methods for real-world problems is still not well understood. We investigate the practicability of one of the fundamental approaches of this field: dynamic programming on tree decompositions. Indisputably, this is a key technique in parameterized algorithms and modern algorithm design. Despite the enormous impact of this approach in theory, it still has very little influence on practical implementations. The reasons for this phenomenon are manifold. One of them is the simple fact that such an implementation requires a long chain of non-trivial tasks (as computing the decomposition, preparing it,...). We provide an easy way to implement such dynamic programs that only requires the definition of the update rules. With this interface, dynamic programs for various problems, such as 3-coloring, can be implemented easily in about 100 lines of structured Java code. The theoretical foundation of the success of dynamic programming on tree decompositions is well understood due to Courcelle's celebrated theorem, which states that every MSO-definable problem can be efficiently solved if a tree decomposition of small width is given. We seek to provide practical access to this theorem as well, by presenting a lightweight model-checker for a small fragment of MSO. This fragment is powerful enough to describe many natural problems, and our model-checker turns out to be very competitive against similar state-of-the-art tools.

Cite as

Max Bannach and Sebastian Berndt. Practical Access to Dynamic Programming on Tree Decompositions. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 6:1-6:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bannach_et_al:LIPIcs.ESA.2018.6,
  author =	{Bannach, Max and Berndt, Sebastian},
  title =	{{Practical Access to Dynamic Programming on Tree Decompositions}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{6:1--6:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.6},
  URN =		{urn:nbn:de:0030-drops-94692},
  doi =		{10.4230/LIPIcs.ESA.2018.6},
  annote =	{Keywords: fixed-parameter tractability, treewidth, model-checking}
}

Document

DOI: 10.4230/LIPIcs.ESA.2018.7

Average Whenever You Meet: Opportunistic Protocols for Community Detection

Authors: Luca Becchetti, Andrea Clementi, Pasin Manurangsi, Emanuele Natale, Francesco Pasquale, Prasad Raghavendra, and Luca Trevisan

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract

Consider the following asynchronous, opportunistic communication model over a graph G: in each round, one edge is activated uniformly and independently at random and (only) its two endpoints can exchange messages and perform local computations. Under this model, we study the following random process: The first time a vertex is an endpoint of an active edge, it chooses a random number, say +/- 1 with probability 1/2; then, in each round, the two endpoints of the currently active edge update their values to their average. We provide a rigorous analysis of the above process showing that, if G exhibits a two-community structure (for example, two expanders connected by a sparse cut), the values held by the nodes will collectively reflect the underlying community structure over a suitable phase of the above process. Our analysis requires new concentration bounds on the product of certain random matrices that are technically challenging and possibly of independent interest. We then exploit our analysis to design the first opportunistic protocols that approximately recover community structure using only logarithmic (or polylogarithmic, depending on the sparsity of the cut) work per node.

Cite as

Luca Becchetti, Andrea Clementi, Pasin Manurangsi, Emanuele Natale, Francesco Pasquale, Prasad Raghavendra, and Luca Trevisan. Average Whenever You Meet: Opportunistic Protocols for Community Detection. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 7:1-7:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{becchetti_et_al:LIPIcs.ESA.2018.7,
  author =	{Becchetti, Luca and Clementi, Andrea and Manurangsi, Pasin and Natale, Emanuele and Pasquale, Francesco and Raghavendra, Prasad and Trevisan, Luca},
  title =	{{Average Whenever You Meet: Opportunistic Protocols for Community Detection}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{7:1--7:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.7},
  URN =		{urn:nbn:de:0030-drops-94705},
  doi =		{10.4230/LIPIcs.ESA.2018.7},
  annote =	{Keywords: Community Detection, Random Processes, Spectral Analysis}
}

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