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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2026.108

On (In)approximability of MaxMin Independent Set Reconfiguration

Authors: Hung P. Hoang, Naoto Ohsaka, Rin Saito, and Yuma Tamura

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract

In the Independent Set Reconfiguration problem under the Token Addition/Removal rule, given a graph G and two independent sets I and J of G, we want to transform I into J by adding and removing vertices, such that all the sets throughout the process are independent sets. Its approximate version called MaxMin Independent Set Reconfiguration aims to maximise the minimum size of the independent sets in the process above. We study the (in)approximability of this problem for general graphs as well as restricted graph classes. Firstly, on general graphs, we obtain a polynomial-time (n / log n)-factor approximation algorithm, complementing the PSPACE-hardness of n^Ω(1)-factor approximation due to Hirahara and Ohsaka [STOC 2024, ICALP 2024] and the NP-hardness of n^{1-ε}-factor approximation due to Ito, Demaine, Harvey, Papadimitriou, Sideri, Uehara, and Uno [TCS 2011]. Secondly, we present a polynomial-time approximation algorithm for degenerate graphs as well as FPT-approximation schemes for bounded-treewidth graphs and H-minor-free graphs. Lastly, we extend the above inapproximability results to bounded-degree graphs, graphs of bandwidth n^{1/2+Θ(1)}, and bipartite graphs.

Cite as

Hung P. Hoang, Naoto Ohsaka, Rin Saito, and Yuma Tamura. On (In)approximability of MaxMin Independent Set Reconfiguration. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 108:1-108:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hoang_et_al:LIPIcs.ICALP.2026.108,
  author =	{Hoang, Hung P. and Ohsaka, Naoto and Saito, Rin and Tamura, Yuma},
  title =	{{On (In)approximability of MaxMin Independent Set Reconfiguration}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{108:1--108:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.108},
  URN =		{urn:nbn:de:0030-drops-264974},
  doi =		{10.4230/LIPIcs.ICALP.2026.108},
  annote =	{Keywords: Combinatorial reconfiguration, independent set, approximation algorithms}
}

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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.2024.38

Basis Sequence Reconfiguration in the Union of Matroids

Authors: Tesshu Hanaka, Yuni Iwamasa, Yasuaki Kobayashi, Yuto Okada, and Rin Saito

Published in: LIPIcs, Volume 322, 35th International Symposium on Algorithms and Computation (ISAAC 2024)

Abstract

Given a graph G and two spanning trees T and T' in G, normalSpanning Tree Reconfiguration asks whether there is a step-by-step transformation from T to T' such that all intermediates are also spanning trees of G, by exchanging an edge in T with an edge outside T at a single step. This problem is naturally related to matroid theory, which shows that there always exists such a transformation for any pair of T and T'. Motivated by this example, we study the problem of transforming a sequence of spanning trees into another sequence of spanning trees. We formulate this problem in the language of matroid theory: Given two sequences of bases of matroids, the goal is to decide whether there is a transformation between these sequences. We design a polynomial-time algorithm for this problem, even if the matroids are given as basis oracles. To complement this algorithmic result, we show that the problem of finding a shortest transformation is NP-hard to approximate within a factor of c log n for some constant c > 0, where n is the total size of the ground sets of the input matroids.

Cite as

Tesshu Hanaka, Yuni Iwamasa, Yasuaki Kobayashi, Yuto Okada, and Rin Saito. Basis Sequence Reconfiguration in the Union of Matroids. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hanaka_et_al:LIPIcs.ISAAC.2024.38,
  author =	{Hanaka, Tesshu and Iwamasa, Yuni and Kobayashi, Yasuaki and Okada, Yuto and Saito, Rin},
  title =	{{Basis Sequence Reconfiguration in the Union of Matroids}},
  booktitle =	{35th International Symposium on Algorithms and Computation (ISAAC 2024)},
  pages =	{38:1--38:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-354-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{322},
  editor =	{Mestre, Juli\'{a}n and Wirth, Anthony},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2024.38},
  URN =		{urn:nbn:de:0030-drops-221658},
  doi =		{10.4230/LIPIcs.ISAAC.2024.38},
  annote =	{Keywords: Combinatorial reconfiguration, Matroids, Polynomial-time algorithm, Inapproximability}
}

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Documents authored by Saito, Rin

On (In)approximability of MaxMin Independent Set Reconfiguration

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Coloring Reconfiguration Under Color Swapping

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Basis Sequence Reconfiguration in the Union of Matroids

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