A Fast Parameterized Algorithm for Co-Path Set
Data Structures and Algorithms
2016-07-29 v3
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 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.
Cite
@article{arxiv.1603.04376,
title = {A Fast Parameterized Algorithm for Co-Path Set},
author = {Blair D. Sullivan and Andrew van der Poel},
journal= {arXiv preprint arXiv:1603.04376},
year = {2016}
}