Polynomial-time algorithm for Maximum Weight Independent Set on P6-free graphs
Abstract
In the classic Maximum Weight Independent Set problem we are given a graph G with a nonnegative weight function on vertices, and the goal is to find an independent set in G of maximum possible weight. While the problem is NP-hard in general, we give a polynomial-time algorithm working on any P6-free graph, that is, a graph that has no path on 6 vertices as an induced subgraph. This improves the polynomial-time algorithm on P5-free graphs of Lokshtanov et al. [11], and the quasipolynomial-time algorithm on P6-free graphs of Lokshtanov et al. [12]. The main technical contribution leading to our main result is enumeration of a polynomial-size family ℱ of vertex subsets with the following property: for every maximal independent set I in the graph, ℱ contains all maximal cliques of some minimal chordal completion of G that does not add any edge incident to a vertex of I.
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Published In
Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms
Pages: 1257 - 1271
Editor: Timothy M. Chan, University of Illinois at Urbana-Champaign, USA
ISBN (Online): 978-1-61197-548-2
Copyright
© 2019 by the Society for Industrial and Applied Mathematics.
History
Published online: 2 January 2019
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