82 Search Results for "Liao, Chung-Shou"

Volume

LIPIcs, Volume 123

29th International Symposium on Algorithms and Computation (ISAAC 2018)

ISAAC 2018, December 16-19, 2018, Jiaoxi, Yilan, Taiwan

Editors: Wen-Lian Hsu, Der-Tsai Lee, and Chung-Shou Liao

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.54
Nearly Optimal Independence Oracle Algorithms for Edge Estimation in Hypergraphs

Authors: Holger Dell, John Lapinskas, and Kitty Meeks

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Consider a query model of computation in which an n-vertex k-hypergraph can be accessed only via its independence oracle or via its colourful independence oracle, and each oracle query may incur a cost depending on the size of the query. Several recent results (Dell and Lapinskas, STOC 2018; Dell, Lapinskas, and Meeks, SODA 2020) give efficient algorithms to approximately count the hypergraph’s edges in the colourful setting. These algorithms immediately imply fine-grained reductions from approximate counting to decision, with overhead only log^Θ(k) n over the running time n^α of the original decision algorithm, for many well-studied problems including k-Orthogonal Vectors, k-SUM, subgraph isomorphism problems including k-Clique and colourful-H, graph motifs, and k-variable first-order model checking. We explore the limits of what is achievable in this setting, obtaining unconditional lower bounds on the oracle cost of algorithms to approximately count the hypergraph’s edges in both the colourful and uncoloured settings. In both settings, we also obtain algorithms which essentially match these lower bounds; in the colourful setting, this requires significant changes to the algorithm of Dell, Lapinskas, and Meeks (SODA 2020) and reduces the total overhead to log^{Θ(k-α)}n. Our lower bound for the uncoloured setting shows that there is no fine-grained reduction from approximate counting to the corresponding uncoloured decision problem (except in the case α ≥ k-1): without an algorithm for the colourful decision problem, we cannot hope to avoid the much larger overhead of roughly n^{(k-α)²/4}. The uncoloured setting has previously been studied for the special case k = 2 (Peled, Ramamoorthy, Rashtchian, Sinha, ITCS 2018; Chen, Levi, and Waingarten, SODA 2020), and our work generalises the existing algorithms and lower bounds for this special case to k > 2 and to oracles with cost.
Cite as

Holger Dell, John Lapinskas, and Kitty Meeks. Nearly Optimal Independence Oracle Algorithms for Edge Estimation in Hypergraphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 54:1-54:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dell_et_al:LIPIcs.ICALP.2024.54,
  author =	{Dell, Holger and Lapinskas, John and Meeks, Kitty},
  title =	{{Nearly Optimal Independence Oracle Algorithms for Edge Estimation in Hypergraphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{54:1--54:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.54},
  URN =		{urn:nbn:de:0030-drops-201977},
  doi =		{10.4230/LIPIcs.ICALP.2024.54},
  annote =	{Keywords: Graph oracles, Fine-grained complexity, Approximate counting, Hypergraphs}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.108
Two-Source and Affine Non-Malleable Extractors for Small Entropy

Authors: Xin Li and Yan Zhong

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Non-malleable extractors are generalizations and strengthening of standard randomness extractors, that are resilient to adversarial tampering. Such extractors have wide applications in cryptography and have become important cornerstones in recent breakthroughs of explicit constructions of two-source extractors and affine extractors for small entropy. However, explicit constructions of non-malleable extractors appear to be much harder than standard extractors. Indeed, in the well-studied models of two-source and affine non-malleable extractors, the previous best constructions only work for entropy rate > 2/3 and 1-γ for some small constant γ > 0 respectively by Li (FOCS' 23). In this paper, we present explicit constructions of two-source and affine non-malleable extractors that match the state-of-the-art constructions of standard ones for small entropy. Our main results include: - Two-source and affine non-malleable extractors (over 𝖥₂) for sources on n bits with min-entropy k ≥ log^C n and polynomially small error, matching the parameters of standard extractors by Chattopadhyay and Zuckerman (STOC' 16, Annals of Mathematics' 19) and Li (FOCS' 16). - Two-source and affine non-malleable extractors (over 𝖥₂) for sources on n bits with min-entropy k = O(log n) and constant error, matching the parameters of standard extractors by Li (FOCS' 23). Our constructions significantly improve previous results, and the parameters (entropy requirement and error) are the best possible without first improving the constructions of standard extractors. In addition, our improved affine non-malleable extractors give strong lower bounds for a certain kind of read-once linear branching programs, recently introduced by Gryaznov, Pudlák, and Talebanfard (CCC' 22) as a generalization of several well studied computational models. These bounds match the previously best-known average-case hardness results given by Chattopadhyay and Liao (CCC' 23) and Li (FOCS' 23), where the branching program size lower bounds are close to optimal, but the explicit functions we use here are different. Our results also suggest a possible deeper connection between non-malleable extractors and standard ones.
Cite as

Xin Li and Yan Zhong. Two-Source and Affine Non-Malleable Extractors for Small Entropy. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 108:1-108:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{li_et_al:LIPIcs.ICALP.2024.108,
  author =	{Li, Xin and Zhong, Yan},
  title =	{{Two-Source and Affine Non-Malleable Extractors for Small Entropy}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{108:1--108:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.108},
  URN =		{urn:nbn:de:0030-drops-202512},
  doi =		{10.4230/LIPIcs.ICALP.2024.108},
  annote =	{Keywords: Randomness Extractors, Non-malleable, Two-source, Affine}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.90
Dynamic PageRank: Algorithms and Lower Bounds

Authors: Rajesh Jayaram, Jakub Łącki, Slobodan Mitrović, Krzysztof Onak, and Piotr Sankowski

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We consider the PageRank problem in the dynamic setting, where the goal is to explicitly maintain an approximate PageRank vector π ∈ ℝⁿ for a graph under a sequence of edge insertions and deletions. Our main result is a complete characterization of the complexity of dynamic PageRank maintenance for both multiplicative and additive (L₁) approximations. First, we establish matching lower and upper bounds for maintaining additive approximate PageRank in both incremental and decremental settings. In particular, we demonstrate that in the worst-case (1/α)^{Θ(log log n)} update time is necessary and sufficient for this problem, where α is the desired additive approximation. On the other hand, we demonstrate that the commonly employed ForwardPush approach performs substantially worse than this optimal runtime. Specifically, we show that ForwardPush requires Ω(n^{1-δ}) time per update on average, for any δ > 0, even in the incremental setting. For multiplicative approximations, however, we demonstrate that the situation is significantly more challenging. Specifically, we prove that any algorithm that explicitly maintains a constant factor multiplicative approximation of the PageRank vector of a directed graph must have amortized update time Ω(n^{1-δ}), for any δ > 0, even in the incremental setting, thereby resolving a 13-year old open question of Bahmani et al. (VLDB 2010). This sharply contrasts with the undirected setting, where we show that poly log n update time is feasible, even in the fully dynamic setting under oblivious adversary.
Cite as

Rajesh Jayaram, Jakub Łącki, Slobodan Mitrović, Krzysztof Onak, and Piotr Sankowski. Dynamic PageRank: Algorithms and Lower Bounds. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 90:1-90:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{jayaram_et_al:LIPIcs.ICALP.2024.90,
  author =	{Jayaram, Rajesh and {\L}\k{a}cki, Jakub and Mitrovi\'{c}, Slobodan and Onak, Krzysztof and Sankowski, Piotr},
  title =	{{Dynamic PageRank: Algorithms and Lower Bounds}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{90:1--90:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.90},
  URN =		{urn:nbn:de:0030-drops-202336},
  doi =		{10.4230/LIPIcs.ICALP.2024.90},
  annote =	{Keywords: PageRank, dynamic algorithms, graph algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.28
Improving the Bounds of the Online Dynamic Power Management Problem

Authors: Ya-Chun Liang, Kazuo Iwama, and Chung-Shou Liao

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

Abstract
We investigate the power-down mechanism which decides when a machine transitions between states such that the total energy consumption, characterized by execution cost, idle cost and switching cost, is minimized. In contrast to most of the previous studies on the offline model, we focus on the online model in which a sequence of jobs with their release time, execution time and deadline, arrive in an online fashion. More precisely, we exploit a different switching on and off strategy and present an upper bound of 3, and further show a lower bound of 2.1, in a dual-machine model, introduced by Chen et al. in 2014 [STACS 2014: 226-238], both of which beat the currently best result.
Cite as

Ya-Chun Liang, Kazuo Iwama, and Chung-Shou Liao. Improving the Bounds of the Online Dynamic Power Management Problem. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{liang_et_al:LIPIcs.ISAAC.2022.28,
  author =	{Liang, Ya-Chun and Iwama, Kazuo and Liao, Chung-Shou},
  title =	{{Improving the Bounds of the Online Dynamic Power Management Problem}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{28:1--28:16},
  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.2022.28},
  URN =		{urn:nbn:de:0030-drops-173138},
  doi =		{10.4230/LIPIcs.ISAAC.2022.28},
  annote =	{Keywords: Online algorithm, Energy scheduling, Dynamic power management}
}
Document
DOI: 10.4230/LIPIcs.ITC.2020.8
Lower Bounds for Function Inversion with Quantum Advice

Authors: Kai-Min Chung, Tai-Ning Liao, and Luowen Qian

Published in: LIPIcs, Volume 163, 1st Conference on Information-Theoretic Cryptography (ITC 2020)

Abstract
Function inversion is the problem that given a random function f: [M] → [N], we want to find pre-image of any image f^{-1}(y) in time T. In this work, we revisit this problem under the preprocessing model where we can compute some auxiliary information or advice of size S that only depends on f but not on y. It is a well-studied problem in the classical settings, however, it is not clear how quantum algorithms can solve this task any better besides invoking Grover’s algorithm [Grover, 1996], which does not leverage the power of preprocessing. Nayebi et al. [Nayebi et al., 2015] proved a lower bound ST² ≥ ̃Ω(N) for quantum algorithms inverting permutations, however, they only consider algorithms with classical advice. Hhan et al. [Minki Hhan et al., 2019] subsequently extended this lower bound to fully quantum algorithms for inverting permutations. In this work, we give the same asymptotic lower bound to fully quantum algorithms for inverting functions for fully quantum algorithms under the regime where M = O(N). In order to prove these bounds, we generalize the notion of quantum random access code, originally introduced by Ambainis et al. [Ambainis et al., 1999], to the setting where we are given a list of (not necessarily independent) random variables, and we wish to compress them into a variable-length encoding such that we can retrieve a random element just using the encoding with high probability. As our main technical contribution, we give a nearly tight lower bound (for a wide parameter range) for this generalized notion of quantum random access codes, which may be of independent interest.
Cite as

Kai-Min Chung, Tai-Ning Liao, and Luowen Qian. Lower Bounds for Function Inversion with Quantum Advice. In 1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 8:1-8:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chung_et_al:LIPIcs.ITC.2020.8,
  author =	{Chung, Kai-Min and Liao, Tai-Ning and Qian, Luowen},
  title =	{{Lower Bounds for Function Inversion with Quantum Advice}},
  booktitle =	{1st Conference on Information-Theoretic Cryptography (ITC 2020)},
  pages =	{8:1--8:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-151-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{163},
  editor =	{Tauman Kalai, Yael and Smith, Adam D. and Wichs, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2020.8},
  URN =		{urn:nbn:de:0030-drops-121134},
  doi =		{10.4230/LIPIcs.ITC.2020.8},
  annote =	{Keywords: Cryptanalysis, Data Structures, Quantum Query Complexity}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.ISAAC.2018
LIPIcs, Volume 123, ISAAC'18, Complete Volume

Authors: Wen-Lian Hsu, Der-Tsai Lee, and Chung-Shou Liao

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
LIPIcs, Volume 123, ISAAC'18, Complete Volume
Cite as

29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Proceedings{hsu_et_al:LIPIcs.ISAAC.2018,
  title =	{{LIPIcs, Volume 123, ISAAC'18, Complete Volume}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018},
  URN =		{urn:nbn:de:0030-drops-101600},
  doi =		{10.4230/LIPIcs.ISAAC.2018},
  annote =	{Keywords: Mathematics of computing, Theory of computation, Data structures design and analysis, Computing methodologies}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.ISAAC.2018.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Wen-Lian Hsu, Der-Tsai Lee, and Chung-Shou Liao

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{hsu_et_al:LIPIcs.ISAAC.2018.0,
  author =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{0:i--0:xviii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.0},
  URN =		{urn:nbn:de:0030-drops-99488},
  doi =		{10.4230/LIPIcs.ISAAC.2018.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ISAAC.2018.1
Going Beyond Traditional Characterizations in the Age of Big Data and Network Sciences (Invited Talk)

Authors: Shang-Hua Teng

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
What are efficient algorithms? What are network models? Big Data and Network Sciences have fundamentally challenged the traditional polynomial-time characterization of efficiency and the conventional graph-theoretical characterization of networks. More than ever before, it is not just desirable, but essential, that efficient algorithms should be scalable. In other words, their complexity should be nearly linear or sub-linear with respect to the problem size. Thus, scalability, not just polynomial-time computability, should be elevated as the central complexity notion for characterizing efficient computation. For a long time, graphs have been widely used for defining the structure of social and information networks. However, real-world network data and phenomena are much richer and more complex than what can be captured by nodes and edges. Network data are multifaceted, and thus network science requires a new theory, going beyond traditional graph theory, to capture the multifaceted data. In this talk, I discuss some aspects of these challenges. Using basic tasks in network analysis, social influence modeling, and machine learning as examples, I highlight the role of scalable algorithms and axiomatization in shaping our understanding of "effective solution concepts" in data and network sciences, which need to be both mathematically meaningful and algorithmically efficient.
Cite as

Shang-Hua Teng. Going Beyond Traditional Characterizations in the Age of Big Data and Network Sciences (Invited Talk). In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{teng:LIPIcs.ISAAC.2018.1,
  author =	{Teng, Shang-Hua},
  title =	{{Going Beyond Traditional Characterizations in the Age of Big Data and Network Sciences}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.1},
  URN =		{urn:nbn:de:0030-drops-99495},
  doi =		{10.4230/LIPIcs.ISAAC.2018.1},
  annote =	{Keywords: scalable algorithms, axiomatization, graph sparsification, local algorithms, advanced sampling, big data, network sciences, machine learning, social influence, beyond graph theory}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ISAAC.2018.2
Approximate Matchings in Massive Graphs via Local Structure (Invited Talk)

Authors: Clifford Stein

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Finding a maximum matching is a fundamental algorithmic problem and is fairly well understood in traditional sequential computing models. Some modern applications require that we handle massive graphs and hence we need to consider algorithms in models that do not allow the entire input graph to be held in the memory of one computer, or models in which the graph is evolving over time. We introduce a new concept called an "Edge Degree Constrained Subgraph (EDCS)", which is a subgraph that is guaranteed to contain a large matching, and which can be identified via local conditions. We then show how to use an EDCS to find 1.5-approximate matchings in several different models including Map Reduce, streaming and distributed computing. We can also use an EDCS to maintain a 1.5-optimal matching in a dynamic graph. This work is joint with Sepehr Asadi, Aaron Bernstein, Mohammad Hossein Bateni and Vahab Marrokni.
Cite as

Clifford Stein. Approximate Matchings in Massive Graphs via Local Structure (Invited Talk). In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{stein:LIPIcs.ISAAC.2018.2,
  author =	{Stein, Clifford},
  title =	{{Approximate Matchings in Massive Graphs via Local Structure}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.2},
  URN =		{urn:nbn:de:0030-drops-99505},
  doi =		{10.4230/LIPIcs.ISAAC.2018.2},
  annote =	{Keywords: matching, dynamic algorithms, parallel algorithms, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.3
Exploiting Sparsity for Bipartite Hamiltonicity

Authors: Andreas Björklund

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
We present a Monte Carlo algorithm that detects the presence of a Hamiltonian cycle in an n-vertex undirected bipartite graph of average degree delta >= 3 almost surely and with no false positives, in (2-2^{1-delta})^{n/2}poly(n) time using only polynomial space. With the exception of cubic graphs, this is faster than the best previously known algorithms. Our method is a combination of a variant of Björklund's 2^{n/2}poly(n) time Monte Carlo algorithm for Hamiltonicity detection in bipartite graphs, SICOMP 2014, and a simple fast solution listing algorithm for very sparse CNF-SAT formulas.
Cite as

Andreas Björklund. Exploiting Sparsity for Bipartite Hamiltonicity. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 3:1-3:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bjorklund:LIPIcs.ISAAC.2018.3,
  author =	{Bj\"{o}rklund, Andreas},
  title =	{{Exploiting Sparsity for Bipartite Hamiltonicity}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{3:1--3:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.3},
  URN =		{urn:nbn:de:0030-drops-99510},
  doi =		{10.4230/LIPIcs.ISAAC.2018.3},
  annote =	{Keywords: Hamiltonian cycle, bipartite graph}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.4
Opinion Forming in Erdös-Rényi Random Graph and Expanders

Authors: Ahad N. Zehmakan

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Assume for a graph G=(V,E) and an initial configuration, where each node is blue or red, in each discrete-time round all nodes simultaneously update their color to the most frequent color in their neighborhood and a node keeps its color in case of a tie. We study the behavior of this basic process, which is called majority model, on the Erdös-Rényi random graph G_{n,p} and regular expanders. First we consider the behavior of the majority model on G_{n,p} with an initial random configuration, where each node is blue independently with probability p_b and red otherwise. It is shown that in this setting the process goes through a phase transition at the connectivity threshold, namely (log n)/n. Furthermore, we say a graph G is lambda-expander if the second-largest absolute eigenvalue of its adjacency matrix is lambda. We prove that for a Delta-regular lambda-expander graph if lambda/Delta is sufficiently small, then the majority model by starting from (1/2-delta)n blue nodes (for an arbitrarily small constant delta>0) results in fully red configuration in sub-logarithmically many rounds. Roughly speaking, this means the majority model is an "efficient" and "fast" density classifier on regular expanders. As a by-product of our results, we show regular Ramanujan graphs are asymptotically optimally immune, that is for an n-node Delta-regular Ramanujan graph if the initial number of blue nodes is s <= beta n, the number of blue nodes in the next round is at most cs/Delta for some constants c,beta>0. This settles an open problem by Peleg [Peleg, 2014].
Cite as

Ahad N. Zehmakan. Opinion Forming in Erdös-Rényi Random Graph and Expanders. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 4:1-4:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{n.zehmakan:LIPIcs.ISAAC.2018.4,
  author =	{N. Zehmakan, Ahad},
  title =	{{Opinion Forming in Erd\"{o}s-R\'{e}nyi Random Graph and Expanders}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{4:1--4:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.4},
  URN =		{urn:nbn:de:0030-drops-99529},
  doi =		{10.4230/LIPIcs.ISAAC.2018.4},
  annote =	{Keywords: majority model, random graph, expander graphs, dynamic monopoly, bootstrap percolation}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.5
Colouring (P_r+P_s)-Free Graphs

Authors: Tereza Klimosová, Josef Malík, Tomás Masarík, Jana Novotná, Daniël Paulusma, and Veronika Slívová

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
The k-Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for a fixed integer k such that no two adjacent vertices are coloured alike. If each vertex u must be assigned a colour from a prescribed list L(u) subseteq {1,...,k}, then we obtain the List k-Colouring problem. A graph G is H-free if G does not contain H as an induced subgraph. We continue an extensive study into the complexity of these two problems for H-free graphs. We prove that List 3-Colouring is polynomial-time solvable for (P_2+P_5)-free graphs and for (P_3+P_4)-free graphs. Combining our results with known results yields complete complexity classifications of 3-Colouring and List 3-Colouring on H-free graphs for all graphs H up to seven vertices. We also prove that 5-Colouring is NP-complete for (P_3+P_5)-free graphs.
Cite as

Tereza Klimosová, Josef Malík, Tomás Masarík, Jana Novotná, Daniël Paulusma, and Veronika Slívová. Colouring (P_r+P_s)-Free Graphs. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 5:1-5:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{klimosova_et_al:LIPIcs.ISAAC.2018.5,
  author =	{Klimosov\'{a}, Tereza and Mal{\'\i}k, Josef and Masar{\'\i}k, Tom\'{a}s and Novotn\'{a}, Jana and Paulusma, Dani\"{e}l and Sl{\'\i}vov\'{a}, Veronika},
  title =	{{Colouring (P\underliner+P\underlines)-Free Graphs}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{5:1--5:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.5},
  URN =		{urn:nbn:de:0030-drops-99533},
  doi =		{10.4230/LIPIcs.ISAAC.2018.5},
  annote =	{Keywords: vertex colouring, H-free graph, linear forest}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.6
The Use of a Pruned Modular Decomposition for Maximum Matching Algorithms on Some Graph Classes

Authors: Guillaume Ducoffe and Alexandru Popa

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
We address the following general question: given a graph class C on which we can solve Maximum Matching in (quasi) linear time, does the same hold true for the class of graphs that can be modularly decomposed into C? As a way to answer this question for distance-hereditary graphs and some other superclasses of cographs, we study the combined effect of modular decomposition with a pruning process over the quotient subgraphs. We remove sequentially from all such subgraphs their so-called one-vertex extensions (i.e., pendant, anti-pendant, twin, universal and isolated vertices). Doing so, we obtain a "pruned modular decomposition", that can be computed in quasi linear time. Our main result is that if all the pruned quotient subgraphs have bounded order then a maximum matching can be computed in linear time. The latter result strictly extends a recent framework in (Coudert et al., SODA'18). Our work is the first to explain why the existence of some nice ordering over the modules of a graph, instead of just over its vertices, can help to speed up the computation of maximum matchings on some graph classes.
Cite as

Guillaume Ducoffe and Alexandru Popa. The Use of a Pruned Modular Decomposition for Maximum Matching Algorithms on Some Graph Classes. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ducoffe_et_al:LIPIcs.ISAAC.2018.6,
  author =	{Ducoffe, Guillaume and Popa, Alexandru},
  title =	{{The Use of a Pruned Modular Decomposition for Maximum Matching Algorithms on Some Graph Classes}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{6:1--6:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.6},
  URN =		{urn:nbn:de:0030-drops-99549},
  doi =		{10.4230/LIPIcs.ISAAC.2018.6},
  annote =	{Keywords: maximum matching, FPT in P, modular decomposition, pruned graphs, one-vertex extensions, P\underline4-structure}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.7
A Novel Algorithm for the All-Best-Swap-Edge Problem on Tree Spanners

Authors: Davide Bilò and Kleitos Papadopoulos

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Given a 2-edge connected, unweighted, and undirected graph G with n vertices and m edges, a sigma-tree spanner is a spanning tree T of G in which the ratio between the distance in T of any pair of vertices and the corresponding distance in G is upper bounded by sigma. The minimum value of sigma for which T is a sigma-tree spanner of G is also called the stretch factor of T. We address the fault-tolerant scenario in which each edge e of a given tree spanner may temporarily fail and has to be replaced by a best swap edge, i.e. an edge that reconnects T-e at a minimum stretch factor. More precisely, we design an O(n^2) time and space algorithm that computes a best swap edge of every tree edge. Previously, an O(n^2 log^4 n) time and O(n^2+m log^2n) space algorithm was known for edge-weighted graphs [Bilò et al., ISAAC 2017]. Even if our improvements on both the time and space complexities are of a polylogarithmic factor, we stress the fact that the design of a o(n^2) time and space algorithm would be considered a breakthrough.
Cite as

Davide Bilò and Kleitos Papadopoulos. A Novel Algorithm for the All-Best-Swap-Edge Problem on Tree Spanners. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 7:1-7:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bilo_et_al:LIPIcs.ISAAC.2018.7,
  author =	{Bil\`{o}, Davide and Papadopoulos, Kleitos},
  title =	{{A Novel Algorithm for the All-Best-Swap-Edge Problem on Tree Spanners}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{7:1--7:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.7},
  URN =		{urn:nbn:de:0030-drops-99557},
  doi =		{10.4230/LIPIcs.ISAAC.2018.7},
  annote =	{Keywords: Transient edge failure, best swap edges, tree spanner}
}
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