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A Fast Parameterized Algorithm for Co-Path Set

Authors Blair D. Sullivan, Andrew van der Poel

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Blair D. Sullivan
Andrew van der Poel

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Blair D. Sullivan and Andrew van der Poel. A Fast Parameterized Algorithm for Co-Path Set. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 28:1-28:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.IPEC.2016.28

Abstract

The k-CO-PATH SET problem asks, given a graph G and a positive integer k, whether one can delete k edges from G so that the remainder is a collection of disjoint paths. We give a linear-time, randomized fpt algorithm with complexity O^*(1.588^k) for deciding k-CO-PATH SET, significantly improving the previously best known O^*(2.17^k) of Feng, Zhou, and Wang (2015). Our main tool is a new O^*(4^{tw(G)}) algorithm for CO-PATH SET using the Cut&Count framework, where tw(G) denotes treewidth. In general graphs, we combine this with a branching algorithm which refines a 6k-kernel into reduced instances, which we prove have bounded treewidth.
Keywords
  • co-path set
  • parameterized complexity
  • Cut&Count
  • bounded treewidth

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