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On (In)approximability of MaxMin Independent Set Reconfiguration

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

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ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Combinatorial reconfiguration
  • independent set
  • approximation algorithms

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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 Get BibTex

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) https://doi.org/10.4230/LIPIcs.ICALP.2026.108

Author Details

Hung P. Hoang
  • Algorithms and Complexity Group, Faculty of Informatics, TU Wien, Austria
Naoto Ohsaka
  • CyberAgent, Inc., Tokyo, Japan
Rin Saito
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Yuma Tamura
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan

Funding

  • Hoang, Hung P.: Austrian Science Foundation (FWF, projects 10.55776/Y1329 and ESP1136425).
  • Saito, Rin: JST SPRING Grant Number JPMJSP2114.
  • Tamura, Yuma: JSPS KAKENHI Grant Number JP25K21148.

Acknowledgements

This work was initiated at the 5th Combinatorial Reconfiguration Workshop (CoRe 2024) in Fukuoka, Japan, in October 2024. We would like to thank the organisers and participants for the inspiring atmosphere. We wish to thank Shuichi Hirahara for helpful conversations. We are also grateful to the anonymous referees for their helpful comments, in particular for pointing out the reference [Bhangale and Khot, 2022], which removes the Unique Games Conjecture assumption in [Austrin et al., 2011].

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