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arXiv · 1905.00340

Independent Set Reconfiguration Parameterized by Modular-Width

Rémy Belmonte·Tesshu Hanaka·Michael Lampis·Hirotaka Ono·Yota Otachi
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Abstract

Independent Set Reconfiguration is one of the most well-studied problems in the setting of combinatorial reconfiguration. It is known that the problem is PSPACE-complete even for graphs of bounded bandwidth. This fact rules out the tractability of parameterizations by most well-studied structural parameters as most of them generalize bandwidth. In this paper, we study the parameterization by modular-width, which is not comparable with bandwidth. We show that the problem parameterized by modular-width is fixed-parameter tractable under all previously studied rules TAR, TJ, and TS. The result under TAR resolves an open problem posed by Bonsma [WG 2014, JGT 2016].

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Rémy Belmonte, Tesshu Hanaka, Michael Lampis, Hirotaka Ono, Yota Otachi. 2019-05-01. Independent Set Reconfiguration Parameterized by Modular-Width. https://arxiv.org/abs/1905.00340

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