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Documents authored by Tamura, Yuma

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.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.SWAT.2024.38
Finding Induced Subgraphs from Graphs with Small Mim-Width

Authors: Yota Otachi, Akira Suzuki, and Yuma Tamura

Published in: LIPIcs, Volume 294, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)

Abstract
In the last decade, algorithmic frameworks based on a structural graph parameter called mim-width have been developed to solve generally NP-hard problems. However, it is known that the frameworks cannot be applied to the Clique problem, and the complexity status of many problems of finding dense induced subgraphs remains open when parameterized by mim-width. In this paper, we investigate the complexity of the problem of finding a maximum induced subgraph that satisfies prescribed properties from a given graph with small mim-width. We first give a meta-theorem implying that various induced subgraph problems are NP-hard for bounded mim-width graphs. Moreover, we show that some problems, including Clique and Induced Cluster Subgraph, remain NP-hard even for graphs with (linear) mim-width at most 2. In contrast to the intractability, we provide an algorithm that, given a graph and its branch decomposition with mim-width at most 1, solves Induced Cluster Subgraph in polynomial time. We emphasize that our algorithmic technique is applicable to other problems such as Induced Polar Subgraph and Induced Split Subgraph. Since a branch decomposition with mim-width at most 1 can be constructed in polynomial time for block graphs, interval graphs, permutation graphs, cographs, distance-hereditary graphs, convex graphs, and their complement graphs, our positive results reveal the polynomial-time solvability of various problems for these graph classes.
Cite as

Yota Otachi, Akira Suzuki, and Yuma Tamura. Finding Induced Subgraphs from Graphs with Small Mim-Width. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{otachi_et_al:LIPIcs.SWAT.2024.38,
  author =	{Otachi, Yota and Suzuki, Akira and Tamura, Yuma},
  title =	{{Finding Induced Subgraphs from Graphs with Small Mim-Width}},
  booktitle =	{19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)},
  pages =	{38:1--38:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-318-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{294},
  editor =	{Bodlaender, Hans L.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2024.38},
  URN =		{urn:nbn:de:0030-drops-200788},
  doi =		{10.4230/LIPIcs.SWAT.2024.38},
  annote =	{Keywords: mim-width, graph algorithm, NP-hardness, induced subgraph problem, cluster vertex deletion}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2020.40
Minimization and Parameterized Variants of Vertex Partition Problems on Graphs

Authors: Yuma Tamura, Takehiro Ito, and Xiao Zhou

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract
Let Π₁, Π₂, …, Π_c be graph properties for a fixed integer c. Then, (Π₁, Π₂, …, Π_c)-Partition is the problem of asking whether the vertex set of a given graph can be partitioned into c subsets V₁, V₂, …, V_c such that the subgraph induced by V_i satisfies the graph property Π_i for every i ∈ {1,2, …, c}. Minimization and parameterized variants of (Π₁, Π₂, …, Π_c)-Partition have been studied for several specific graph properties, where the size of the vertex subset V₁ satisfying Π₁ is minimized or taken as a parameter. In this paper, we first show that the minimization variant is hard to approximate for any nontrivial additive hereditary graph properties, unless c = 2 and both Π₁ and Π₂ are classes of edgeless graphs. We then give FPT algorithms for the parameterized variant when restricted to the case where c = 2, Π₁ is a hereditary graph property, and Π₂ is the class of acyclic graphs.
Cite as

Yuma Tamura, Takehiro Ito, and Xiao Zhou. Minimization and Parameterized Variants of Vertex Partition Problems on Graphs. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 40:1-40:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{tamura_et_al:LIPIcs.ISAAC.2020.40,
  author =	{Tamura, Yuma and Ito, Takehiro and Zhou, Xiao},
  title =	{{Minimization and Parameterized Variants of Vertex Partition Problems on Graphs}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{40:1--40:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.40},
  URN =		{urn:nbn:de:0030-drops-133844},
  doi =		{10.4230/LIPIcs.ISAAC.2020.40},
  annote =	{Keywords: Graph Algorithms, Approximability, Fixed-Parameter Tractability, Vertex Partition Problem, Feedback Vertex Set Problem}
}
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