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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

DOI: 10.4230/LIPIcs.ISAAC.2025.22

Minimum Partition of Polygons Under Width and Cut Constraints

Authors: Jaehoon Chung, Kazuo Iwama, Chung-Shou Liao, and Hee-Kap Ahn

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract

We study the problem of partitioning a polygon into the minimum number of subpolygons using cuts in predetermined directions such that each resulting subpolygon satisfies a given width constraint. A polygon satisfies the unit-width constraint for a set of unit vectors if the length of the orthogonal projection of the polygon on a line parallel to a vector in the set is at most one. We analyze structural properties of the minimum partition numbers, focusing on monotonicity under polygon containment. We show that the minimum partition number of a simple polygon is at least that of any subpolygon, provided that the subpolygon satisfies a certain orientation-wise convexity with respect to the polygon. As a consequence, we prove a partition analogue of the Bang’s conjecture about coverings of convex regions in the plane: for any partition of a convex body in the plane, the sum of relative widths of all parts is at least one. For any convex polygon, there exists a direction along which an optimal partition is achieved by parallel cuts. Given such a direction, an optimal partition can be computed in linear time.

Cite as

Jaehoon Chung, Kazuo Iwama, Chung-Shou Liao, and Hee-Kap Ahn. Minimum Partition of Polygons Under Width and Cut Constraints. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chung_et_al:LIPIcs.ISAAC.2025.22,
  author =	{Chung, Jaehoon and Iwama, Kazuo and Liao, Chung-Shou and Ahn, Hee-Kap},
  title =	{{Minimum Partition of Polygons Under Width and Cut Constraints}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{22:1--22:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.22},
  URN =		{urn:nbn:de:0030-drops-249302},
  doi =		{10.4230/LIPIcs.ISAAC.2025.22},
  annote =	{Keywords: Polygon partitioning, Width constraints, Plank problem}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2025.23

Precoloring Extension with Demands on Paths

Authors: Arun Kumar Das, Michal Opler, and Tomáš Valla

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract

Let G be a graph with a set of precolored vertices, and let us be given an integer distance parameter d and a set of integer demands d₁,… ,d_c. The Distance Precoloring Extension with Demands (DPED) problem is to compute a vertex c-coloring of G such that the following three conditions hold: (i) the resulting coloring respects the colors of the precolored vertices, (ii) the distance of two vertices of the same color is at least d, and (iii) the number of vertices colored by color i is exactly d_i. This problem is motivated by a program scheduling in commercial broadcast channels with constraints on content repetition and placement, which leads precisely to the DPED problem for paths. In this paper, we study DPED on paths and present a polynomial time exact algorithm when precolored vertices are restricted to the two ends of the path and devise an approximation algorithm for DPED with an additive approximation factor polynomially bounded by d and the number of precolored vertices. Then, we prove that the Distance Precoloring Extension problem on paths, a less restrictive version of DPED without the demand constraints, and then DPED itself, is NP-complete. Motivated by this result, we further study the parameterized complexity of DPED on paths. We establish that the DPED problem on paths is W[1]-hard when parameterized by the number of colors and the distance. On the positive side, we devise a fixed parameter tractable (FPT) algorithm for DPED on paths when the number of colors, the distance, and the number of precolored vertices are considered as the parameters. Moreover, we prove that Distance Precoloring Extension is FPT parameterized by the distance. As a byproduct, we also obtain several results for the Distance List Coloring problem on paths.

Cite as

Arun Kumar Das, Michal Opler, and Tomáš Valla. Precoloring Extension with Demands on Paths. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{das_et_al:LIPIcs.ISAAC.2025.23,
  author =	{Das, Arun Kumar and Opler, Michal and Valla, Tom\'{a}\v{s}},
  title =	{{Precoloring Extension with Demands on Paths}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{23:1--23:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.23},
  URN =		{urn:nbn:de:0030-drops-249319},
  doi =		{10.4230/LIPIcs.ISAAC.2025.23},
  annote =	{Keywords: precoloring extension, distance coloring, FPT, approximation algorithms}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2024.69

Scheduling with Locality by Routing

Authors: Alison Hsiang-Hsuan Liu and Fu-Hong Liu

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract

This work examines a strongly NP-hard routing problem on trees, in which multiple servers need to serve a given set of requests (on vertices), where the routes of the servers start from a common source and end at their respective terminals. Each server can travel free of cost on its source-to-terminal path but has to pay for travel on other edges. The objective is to minimize the maximum cost over all servers. As the servers may pay different costs for traveling through a common edge, balancing the loads of the servers can be difficult. We propose a polynomial-time 4-approximation algorithm that applies the parametric pruning framework but consists of two phases. The first phase of the algorithm partitions the requests into packets, and the second phase of the algorithm assigns the packets to the servers. Unlike the standard parametric pruning techniques, the challenge of our algorithm design and analysis is to harmoniously relate the quality of the partition in the first phase, the balances of the servers' loads in the second phase, and the hypothetical optimal values of the framework. For the problem in general graphs, we show that there is no algorithm better than 2-approximate unless P = NP. The problem is a generalization of unrelated machine scheduling and other classic scheduling problems. It also models scheduling problems where the job processing times depend on the machine serving the job and the other jobs served by that machine. This modeling provides a framework that physicalizes scheduling problems through the graph’s point of view.

Cite as

Alison Hsiang-Hsuan Liu and Fu-Hong Liu. Scheduling with Locality by Routing. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 69:1-69:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{liu_et_al:LIPIcs.MFCS.2024.69,
  author =	{Liu, Alison Hsiang-Hsuan and Liu, Fu-Hong},
  title =	{{Scheduling with Locality by Routing}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{69:1--69:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.69},
  URN =		{urn:nbn:de:0030-drops-206250},
  doi =		{10.4230/LIPIcs.MFCS.2024.69},
  annote =	{Keywords: Makespan minimization, Approximation algorithms, Routing problems, Parametric pruning framework}
}

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

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.2018.6

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.

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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}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2018.8

Efficient Enumeration of Dominating Sets for Sparse Graphs

Authors: Kazuhiro Kurita, Kunihiro Wasa, Hiroki Arimura, and Takeaki Uno

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

Abstract

A dominating set D of a graph G is a set of vertices such that any vertex in G is in D or its neighbor is in D. Enumeration of minimal dominating sets in a graph is one of central problems in enumeration study since enumeration of minimal dominating sets corresponds to enumeration of minimal hypergraph transversal. However, enumeration of dominating sets including non-minimal ones has not been received much attention. In this paper, we address enumeration problems for dominating sets from sparse graphs which are degenerate graphs and graphs with large girth, and we propose two algorithms for solving the problems. The first algorithm enumerates all the dominating sets for a k-degenerate graph in O(k) time per solution using O(n + m) space, where n and m are respectively the number of vertices and edges in an input graph. That is, the algorithm is optimal for graphs with constant degeneracy such as trees, planar graphs, H-minor free graphs with some fixed H. The second algorithm enumerates all the dominating sets in constant time per solution for input graphs with girth at least nine.

Cite as

Kazuhiro Kurita, Kunihiro Wasa, Hiroki Arimura, and Takeaki Uno. Efficient Enumeration of Dominating Sets for Sparse Graphs. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{kurita_et_al:LIPIcs.ISAAC.2018.8,
  author =	{Kurita, Kazuhiro and Wasa, Kunihiro and Arimura, Hiroki and Uno, Takeaki},
  title =	{{Efficient Enumeration of Dominating Sets for Sparse Graphs}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{8:1--8:13},
  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.2018.8},
  URN =		{urn:nbn:de:0030-drops-99560},
  doi =		{10.4230/LIPIcs.ISAAC.2018.8},
  annote =	{Keywords: Enumeration algorithm, polynomial amortized time, dominating set, girth, degeneracy}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2018.9

Complexity of Unordered CNF Games

Authors: Md Lutfar Rahman and Thomas Watson

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

Abstract

The classic TQBF problem is to determine who has a winning strategy in a game played on a given CNF formula, where the two players alternate turns picking truth values for the variables in a given order, and the winner is determined by whether the CNF gets satisfied. We study variants of this game in which the variables may be played in any order, and each turn consists of picking a remaining variable and a truth value for it. - For the version where the set of variables is partitioned into two halves and each player may only pick variables from his/her half, we prove that the problem is PSPACE-complete for 5-CNFs and in P for 2-CNFs. Previously, it was known to be PSPACE-complete for unbounded-width CNFs (Schaefer, STOC 1976). - For the general unordered version (where each variable can be picked by either player), we also prove that the problem is PSPACE-complete for 5-CNFs and in P for 2-CNFs. Previously, it was known to be PSPACE-complete for 6-CNFs (Ahlroth and Orponen, MFCS 2012) and PSPACE-complete for positive 11-CNFs (Schaefer, STOC 1976).

Cite as

Md Lutfar Rahman and Thomas Watson. Complexity of Unordered CNF Games. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 9:1-9:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{rahman_et_al:LIPIcs.ISAAC.2018.9,
  author =	{Rahman, Md Lutfar and Watson, Thomas},
  title =	{{Complexity of Unordered CNF Games}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{9:1--9:12},
  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.2018.9},
  URN =		{urn:nbn:de:0030-drops-99574},
  doi =		{10.4230/LIPIcs.ISAAC.2018.9},
  annote =	{Keywords: CNF, Games, PSPACE-complete, SAT, Linear Time}
}

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