9 Search Results for "Hoang, Duc A."

Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.31
Token Sliding Independent Set Reconfiguration on Block Graphs

Authors: Mathew C. Francis and Veena Prabhakaran

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
Let S be an independent set of a simple undirected graph G. Suppose that each vertex of S has a token placed on it. The tokens are allowed to be moved, one at a time, by sliding along the edges of G while maintaining the property that after each move, the vertices having tokens always form an independent set of G. We would like to determine whether the tokens can be eventually brought to stay on the vertices of another independent set S' of G in this manner. In other words, we would like to decide if we can transform S into S' through a sequence of steps, each of which involves substituting a vertex in the current independent set with one of its neighbours to obtain another independent set. This problem of determining if one independent set of a graph "is reachable" from another independent set of it is known to be PSPACE-hard even for split graphs, planar graphs, and graphs of bounded treewidth. Polynomial time algorithms have been obtained for certain graph classes like trees, interval graphs, claw-free graphs, and bipartite permutation graphs. We present a polynomial time algorithm for the problem on block graphs, which are the graphs in which every maximal 2-connected subgraph is a clique. Our algorithm is the first generalization of the known polynomial time algorithm for trees to a larger class of graphs.
Cite as

Mathew C. Francis and Veena Prabhakaran. Token Sliding Independent Set Reconfiguration on Block Graphs. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{francis_et_al:LIPIcs.FSTTCS.2025.31,
  author =	{Francis, Mathew C. and Prabhakaran, Veena},
  title =	{{Token Sliding Independent Set Reconfiguration on Block Graphs}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{31:1--31:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.31},
  URN =		{urn:nbn:de:0030-drops-251120},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.31},
  annote =	{Keywords: Token sliding independent set reconfiguration, block graphs, polynomial time algorithm}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.39
Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules

Authors: Shuichi Hirahara, Naoto Ohsaka, Tatsuhiro Suga, Akira Suzuki, Yuma Tamura, and Xiao Zhou

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

Abstract
In reconfiguration problems, we are given two feasible solutions to a graph problem and asked whether one can be transformed into the other via a sequence of feasible intermediate solutions under a given reconfiguration rule. While earlier work focused on modifying a single element at a time, recent studies have started examining how different rules impact computational complexity. Motivated by recent progress, we study Independent Set Reconfiguration (ISR) and Vertex Cover Reconfiguration (VCR) under the k-Token Jumping (k-TJ) and k-Token Sliding (k-TS) models. In k-TJ, up to k vertices may be replaced, while k-TS additionally requires a perfect matching between removed and added vertices. It is known that the complexity of ISR crucially depends on k, ranging from PSPACE-complete and NP-complete to polynomial-time solvable. In this paper, we further explore the gradient of computational complexity of the problems. We first show that ISR under k-TJ with k = |I| - μ remains NP-hard when μ is any fixed positive integer and the input graph is restricted to graphs of maximum degree 3 or planar graphs of maximum degree 4, where |I| is the size of feasible solutions. In addition, we prove that the problem belongs to NP not only for μ = O(1) but also for μ = O(log |I|). In contrast, we show that VCR under k-TJ is in XP when parameterized by μ = |S| - k, where |S| is the size of feasible solutions. Furthermore, we establish the PSPACE-completeness of ISR and VCR under both k-TJ and k-TS on several graph classes, for fixed k as well as superconstant k relative to the size of feasible solutions.
Cite as

Shuichi Hirahara, Naoto Ohsaka, Tatsuhiro Suga, Akira Suzuki, Yuma Tamura, and Xiao Zhou. Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hirahara_et_al:LIPIcs.ISAAC.2025.39,
  author =	{Hirahara, Shuichi and Ohsaka, Naoto and Suga, Tatsuhiro and Suzuki, Akira and Tamura, Yuma and Zhou, Xiao},
  title =	{{Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{39:1--39:20},
  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.2025.39},
  URN =		{urn:nbn:de:0030-drops-249474},
  doi =		{10.4230/LIPIcs.ISAAC.2025.39},
  annote =	{Keywords: combinatorial reconfiguration, extended reconfiguration rule, independent set reconfiguration, vertex cover reconfiguration, PSPACE-completeness, NP-completeness}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.33
Coloring Reconfiguration Under Color Swapping

Authors: Janosch Fuchs, Rin Saito, Tatsuhiro Suga, Takahiro Suzuki, and Yuma Tamura

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

Abstract
In the Coloring Reconfiguration problem, we are given two proper k-colorings of a graph and asked to decide whether one can be transformed into the other by repeatedly applying a specified recoloring rule, while maintaining a proper coloring throughout. For this problem, two recoloring rules have been widely studied: single-vertex recoloring and Kempe chain recoloring. In this paper, we introduce a new rule, called color swapping, where two adjacent vertices may exchange their colors, so that the resulting coloring remains proper, and study the computational complexity of the problem under this rule. We first establish a complexity dichotomy with respect to k: the problem is solvable in polynomial time for k ≤ 2, and is PSPACE-complete for k ≥ 3. We further show that the problem remains PSPACE-complete even on restricted graph classes, including bipartite graphs, split graphs, and planar graphs of bounded degree. In contrast, we present polynomial-time algorithms for several graph classes: for paths when k = 3, for split graphs when k is fixed, and for cographs when k is arbitrary.
Cite as

Janosch Fuchs, Rin Saito, Tatsuhiro Suga, Takahiro Suzuki, and Yuma Tamura. Coloring Reconfiguration Under Color Swapping. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fuchs_et_al:LIPIcs.ISAAC.2025.33,
  author =	{Fuchs, Janosch and Saito, Rin and Suga, Tatsuhiro and Suzuki, Takahiro and Tamura, Yuma},
  title =	{{Coloring Reconfiguration Under Color Swapping}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{33:1--33:21},
  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.2025.33},
  URN =		{urn:nbn:de:0030-drops-249411},
  doi =		{10.4230/LIPIcs.ISAAC.2025.33},
  annote =	{Keywords: Combinatorial reconfiguration, graph coloring, PSPACE-complete, graph algorithm}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.29
The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration

Authors: Nicolas Bousquet, Quentin Deschamps, Arnaud Mary, Amer E. Mouawad, and Théo Pierron

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
A dominating set of a graph G = (V,E) is a set of vertices D ⊆ V whose closed neighborhood is V, i.e., N[D] = V. We view a dominating set as a collection of tokens placed on the vertices of D. In the token sliding variant of the Dominating Set Reconfiguration problem (TS-DSR), we seek to transform a source dominating set into a target dominating set in G by sliding tokens along edges, and while maintaining a dominating set all along the transformation. TS-DSR is known to be PSPACE-complete even restricted to graphs of pathwidth w, for some non-explicit constant w and to be XL-complete parameterized by the size k of the solution. The first contribution of this article consists in using a novel approach to provide the first explicit constant for which the TS-DSR problem is PSPACE-complete, a question that was left open in the literature. From a parameterized complexity perspective, the token jumping variant of DSR, i.e., where tokens can jump to arbitrary vertices, is known to be FPT when parameterized by the size of the dominating sets on nowhere dense classes of graphs. But, in contrast, no non-trivial result was known about TS-DSR. We prove that DSR is actually much harder in the sliding model since it is XL-complete when restricted to bounded pathwidth graphs and even when parameterized by k plus the feedback vertex set number of the graph. This gives, for the first time, a difference of behavior between the complexity under token sliding and token jumping for some problem on graphs of bounded treewidth. All our results are obtained using a brand new method, based on the hardness of the so-called Tape Reconfiguration problem, a problem we believe to be of independent interest. We complement these hardness results with a positive result showing that DSR (parameterized by k) in the sliding model is FPT on planar graphs, also answering an open problem from the literature.
Cite as

Nicolas Bousquet, Quentin Deschamps, Arnaud Mary, Amer E. Mouawad, and Théo Pierron. The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bousquet_et_al:LIPIcs.ESA.2025.29,
  author =	{Bousquet, Nicolas and Deschamps, Quentin and Mary, Arnaud and Mouawad, Amer E. and Pierron, Th\'{e}o},
  title =	{{The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{29:1--29:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.29},
  URN =		{urn:nbn:de:0030-drops-244974},
  doi =		{10.4230/LIPIcs.ESA.2025.29},
  annote =	{Keywords: combinatorial reconfiguration, parameterized complexity, structural graph parameters, treewidth, dominating set}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.41
Token Sliding Reconfiguration on DAGs

Authors: Jona Dirks and Alexandre Vigny

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Given a graph G and two independent sets of same size, the Independent Set Reconfiguration Problem under token sliding asks whether one can, in a step by step manner, transform the first independent set into the second one. In each step we must preserve the condition of independence. Further, referring to solution vertices as tokens, we are only permitted to slide a token along an edge. Until the recent work of Ito et al. [Ito et al. MFCS 2022] this problem was only considered on undirected graphs. In this work, we study reconfiguration under token sliding focusing on DAGs. We present a complete dichotomy of intractability in regard to the depth of the DAG, by proving that this problem is NP-complete for DAGs of depth 3 and W[1]-hard for depth 4 when parameterized by the number of tokens k, and that these bounds are tight. Further, we prove that it is fixed parameter tractable on DAGs parameterized by the combination of treewidth and k. We show that this result applies to undirected graphs, when the number of times a token can visit a vertex is restricted.
Cite as

Jona Dirks and Alexandre Vigny. Token Sliding Reconfiguration on DAGs. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 41:1-41:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dirks_et_al:LIPIcs.MFCS.2025.41,
  author =	{Dirks, Jona and Vigny, Alexandre},
  title =	{{Token Sliding Reconfiguration on DAGs}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{41:1--41:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.41},
  URN =		{urn:nbn:de:0030-drops-241486},
  doi =		{10.4230/LIPIcs.MFCS.2025.41},
  annote =	{Keywords: Graph theory, FPT algorithms, Reconfiguration, Independent Sets}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.96
Asymptotically Optimal Inapproximability of Maxmin k-Cut Reconfiguration

Authors: Shuichi Hirahara and Naoto Ohsaka

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
k-Coloring Reconfiguration is one of the most well-studied reconfiguration problems, which asks to transform a given proper k-coloring of a graph to another by repeatedly recoloring a single vertex. Its approximate version, Maxmin k-Cut Reconfiguration, is defined as an optimization problem of maximizing the minimum fraction of bichromatic edges during the transformation between (not necessarily proper) k-colorings. In this paper, we demonstrate that the optimal approximation factor of this problem is 1 - Θ(1/k) for every k ≥ 2. Specifically, we prove the PSPACE-hardness of approximating the objective value within a factor of 1 - ε/k for some universal constant ε > 0, whereas we develop a deterministic polynomial-time algorithm that achieves the approximation factor of 1 - 2/k. To prove the hardness result, we propose a new probabilistic verifier that tests a "striped" pattern. Our approximation algorithm is based on a random transformation that passes through a random k-coloring.
Cite as

Shuichi Hirahara and Naoto Ohsaka. Asymptotically Optimal Inapproximability of Maxmin k-Cut Reconfiguration. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 96:1-96:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hirahara_et_al:LIPIcs.ICALP.2025.96,
  author =	{Hirahara, Shuichi and Ohsaka, Naoto},
  title =	{{Asymptotically Optimal Inapproximability of Maxmin k-Cut Reconfiguration}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{96:1--96:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l 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.2025.96},
  URN =		{urn:nbn:de:0030-drops-234733},
  doi =		{10.4230/LIPIcs.ICALP.2025.96},
  annote =	{Keywords: reconfiguration problems, graph coloring, hardness of approximation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.122
Yet Another Simple Proof of the PCRP Theorem

Authors: Naoto Ohsaka

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
The Probabilistically Checkable Reconfiguration Proof (PCRP) theorem, proven by Hirahara and Ohsaka (STOC 2024) [Hirahara and Ohsaka, 2024] and Karthik C. S. and Manurangsi [{Karthik {C. S.}} and Manurangsi, 2023], provides a new PCP-type characterization of PSPACE: A language L is in PSPACE if and only if there exists a probabilistic verifier 𝒱 and a pair of polynomial-time computable proofs π^ini, π^end such that the following hold for every input x: - If x ∈ L, then π^ini(x) can be transformed into π^end(x) by repeatedly flipping a single bit of the proof at a time, while making 𝒱(x) to accept every intermediate proof with probability 1. - If x ∉ L, then any such transformation induces a proof that is rejected by 𝒱(x) with probability more than 1/2. The PCRP theorem finds many applications in PSPACE-hardness of approximation for reconfiguration problems. In this paper, we present an alternative proof of the PCRP theorem that is "simpler" than those of Hirahara and Ohsaka [Hirahara and Ohsaka, 2024] and Karthik C. S. and Manurangsi [Karthik C. S. and Manurangsi, 2023]. Our PCRP system is obtained by combining simple robustization and composition steps in a modular fashion, which renders its analysis more intuitive. The crux of implementing the robustization step is an error-correcting code that enjoys both list decodability and reconfigurability, the latter of which enables to reconfigure between a pair of codewords, while avoiding getting too close to any other codewords.
Cite as

Naoto Ohsaka. Yet Another Simple Proof of the PCRP Theorem. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 122:1-122:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ohsaka:LIPIcs.ICALP.2025.122,
  author =	{Ohsaka, Naoto},
  title =	{{Yet Another Simple Proof of the PCRP Theorem}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{122:1--122:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l 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.2025.122},
  URN =		{urn:nbn:de:0030-drops-234995},
  doi =		{10.4230/LIPIcs.ICALP.2025.122},
  annote =	{Keywords: reconfiguration problems, hardness of approximation, probabilistic proof systems}
}
Document
Survey
DOI: 10.4230/TGDK.1.1.12
Structural Summarization of Semantic Graphs Using Quotients

Authors: Ansgar Scherp, David Richerby, Till Blume, Michael Cochez, and Jannik Rau

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract
Graph summarization is the process of computing a compact version of an input graph while preserving chosen features of its structure. We consider semantic graphs where the features include edge labels and label sets associated with a vertex. Graph summaries are typically much smaller than the original graph. Applications that depend on the preserved features can perform their tasks on the summary, but much faster or with less memory overhead, while producing the same outcome as if they were applied on the original graph. In this survey, we focus on structural summaries based on quotients that organize vertices in equivalence classes of shared features. Structural summaries are particularly popular for semantic graphs and have the advantage of defining a precise graph-based output. We consider approaches and algorithms for both static and temporal graphs. A common example of quotient-based structural summaries is bisimulation, and we discuss this in detail. While there exist other surveys on graph summarization, to the best of our knowledge, we are the first to bring in a focused discussion on quotients, bisimulation, and their relation. Furthermore, structural summarization naturally connects well with formal logic due to the discrete structures considered. We complete the survey with a brief description of approaches beyond structural summaries.
Cite as

Ansgar Scherp, David Richerby, Till Blume, Michael Cochez, and Jannik Rau. Structural Summarization of Semantic Graphs Using Quotients. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 12:1-12:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{scherp_et_al:TGDK.1.1.12,
  author =	{Scherp, Ansgar and Richerby, David and Blume, Till and Cochez, Michael and Rau, Jannik},
  title =	{{Structural Summarization of Semantic Graphs Using Quotients}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{12:1--12:25},
  ISSN =	{2942-7517},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.12},
  URN =		{urn:nbn:de:0030-drops-194862},
  doi =		{10.4230/TGDK.1.1.12},
  annote =	{Keywords: graph summarization, quotients, stratified bisimulation}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2016.37
Sliding Tokens on a Cactus

Authors: Duc A. Hoang and Ryuhei Uehara

Published in: LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016)

Abstract
Given two independent sets I and J of a graph G, imagine that a token (coin) is placed on each vertex in I. Then, the Sliding Token problem asks if one could transforms I to J using a sequence of elementary steps, where each step requires sliding a token from one vertex to one of its neighbors, such that the resulting set of vertices where tokens are placed still remains independent. In this paper, we describe a polynomial-time algorithm for solving Sliding Token in case the graph G is a cactus. Our algorithm is designed based on two observations. First, all structures that forbid the existence of a sequence of token slidings between I and J, if exist, can be found in polynomial time. A no-instance may be easily deduced using this characterization. Second, without such forbidden structures, a sequence of token slidings between I and J does exist.
Cite as

Duc A. Hoang and Ryuhei Uehara. Sliding Tokens on a Cactus. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 37:1-37:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{hoang_et_al:LIPIcs.ISAAC.2016.37,
  author =	{Hoang, Duc A. and Uehara, Ryuhei},
  title =	{{Sliding Tokens on a Cactus}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{37:1--37:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Hong, Seok-Hee},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.37},
  URN =		{urn:nbn:de:0030-drops-68074},
  doi =		{10.4230/LIPIcs.ISAAC.2016.37},
  annote =	{Keywords: reconfiguration problem, token sliding, independent set, cactus}
}
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