LIPIcs.ISAAC.2024.36.pdf
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Kernelization Complexity of Solution Discovery Problems
Authors
Mario Grobler 
,
Stephanie Maaz ,
Amer E. Mouawad ,
Naomi Nishimura ,
Vijayaragunathan Ramamoorthi ,
Sebastian Siebertz
-
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35th International Symposium on Algorithms and Computation (ISAAC 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Symposium on Algorithms and Computation (ISAAC) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-12-04
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Mario Grobler, Stephanie Maaz, Amer E. Mouawad, Naomi Nishimura, Vijayaragunathan Ramamoorthi, and Sebastian Siebertz. Kernelization Complexity of Solution Discovery Problems. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ISAAC.2024.36
Abstract
In the solution discovery variant of a vertex (edge) subset problem Π on graphs, we are given an initial configuration of tokens on the vertices (edges) of an input graph G together with a budget b. The question is whether we can transform this configuration into a feasible solution of Π on G with at most b modification steps. We consider the token sliding variant of the solution discovery framework, where each modification step consists of sliding a token to an adjacent vertex (edge). The framework of solution discovery was recently introduced by Fellows et al. [ECAI 2023] and for many solution discovery problems the classical as well as the parameterized complexity has been established. In this work, we study the kernelization complexity of the solution discovery variants of Vertex Cover, Independent Set, Dominating Set, Shortest Path, Matching, and Vertex Cut with respect to the parameters number of tokens k, discovery budget b, as well as structural parameters such as pathwidth.
Subject Classification
ACM Subject Classification
- Mathematics of computing → Graph algorithms
- Theory of computation → Fixed parameter tractability
- Mathematics of computing → Combinatorics
Keywords
- solution discovery
- kernelization
- cut
- independent set
- vertex cover
- dominating set
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References
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