Scalable Hard Instances for Independent Set Reconfiguration

Authors Takehide Soh , Takumu Watanabe, Jun Kawahara , Akira Suzuki , Takehiro Ito

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Takehide Soh
  • Information Infrastructure and Digital Transformation Initiatives Headquaters, Kobe University, Japan
Takumu Watanabe
  • Graduate School of Information Sciences, Tohoku University, Japan
Jun Kawahara
  • Graduate School of Informatics, Kyoto University, Japan
Akira Suzuki
  • Graduate School of Information Sciences, Tohoku University, Japan
Takehiro Ito
  • Graduate School of Information Sciences, Tohoku University, Japan

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Takehide Soh, Takumu Watanabe, Jun Kawahara, Akira Suzuki, and Takehiro Ito. Scalable Hard Instances for Independent Set Reconfiguration. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


The Token Jumping problem, also known as the independent set reconfiguration problem under the token jumping model, is defined as follows: Given a graph and two same-sized independent sets, determine whether one can be transformed into the other via a sequence of independent sets. Token Jumping has been extensively studied, mainly from the viewpoint of algorithmic theory, but its practical study has just begun. To develop a practically good solver, it is important to construct benchmark datasets that are scalable and hard. Here, "scalable" means the ability to change the scale of the instance while maintaining its characteristics by adjusting the given parameters; and "hard" means that the instance can become so difficult that it cannot be solved within a practical time frame by a solver. In this paper, we propose four types of instance series for Token Jumping. Our instance series is scalable in the sense that instance scales are controlled by the number of vertices. To establish their hardness, we focus on the numbers of transformation steps; our instance series requires exponential numbers of steps with respect to the number of vertices. Interestingly, three types of instance series are constructed by importing theories developed by algorithmic research. We experimentally evaluate the scalability and hardness of the proposed instance series, using the SAT solver and award-winning solvers of the international competition for Token Jumping.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Discrete space search
  • Combinatorial reconfiguration
  • Benckmark dataset
  • Graph Algorithm
  • PSPACE-complete


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