Parameterized Complexities of Dominating and Independent Set Reconfiguration

Hans L. Bodlaender; Carla Groenland; Céline M. F. Swennenhuis

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arXiv · 2106.15907

Parameterized Complexities of Dominating and Independent Set Reconfiguration

Hans L. Bodlaender·Carla Groenland·Céline M. F. Swennenhuis

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Abstract

We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on the number of moves, XNL-complete when a maximum length $\ell$ for the sequence is given in binary in the input, and XNLP-complete when $\ell$ is given in unary. The problems were known to be $\mathrm{W}[1]$- and $\mathrm{W}[2]$-hard respectively when $\ell$ is also a parameter. We complete the picture by showing membership in those classes. Moreover, we show that for all the variants that we consider, token sliding and token jumping are equivalent under pl-reductions. We introduce partitioned variants of token jumping and token sliding, and give pl-reductions between the four variants that have precise control over the number of tokens and the length of the reconfiguration sequence.

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BibTeX RIS

Hans L. Bodlaender, Carla Groenland, Céline M. F. Swennenhuis. 2021-06-30. Parameterized Complexities of Dominating and Independent Set Reconfiguration. https://arxiv.org/abs/2106.15907

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