Year: 2026
Type: preprint
Abstract: In a directed graph, a stable (or acyclic) set is a set which does not induce a directed cycle. Given a directed graph and two acyclic sets of the same size, the Acyclic-Set-Reconfiguration with Directed Token Sliding (ASR) problem asks whether one can, by iteratively replacing a vertex by an adjacent one, transform the first set into the second one, while maintaining acyclicity during the transformation. In this work, we present a study of the complexity of ASR and provide an FPT algorithm for semi-complete digraphs, when parametrized by the size of the sets being reconfigured, the directed pathwidth (or equivalently, the directed treewidth) of the instance, and a newly introduced parameter called the iteration of the reconfiguration sequence. To the best of our knowledge, the reconfiguration of stable sets has only been studied on undirected graphs, or (more recently) on sparse directed graphs.
Source: arXiv (Cornell University)
Institutions: National Institute of Informatics, The Graduate University for Advanced Studies, SOKENDAI, Centre National de la Recherche Scientifique, Université Côte d'Azur, Institut polytechnique de Grenoble, Laboratoire des Sciences pour la Conception, l'Optimisation et la Production, Université Grenoble Alpes, Université Clermont Auvergne
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223695530