The Parameterized Complexity of the Minimum Shared Edges Problem
Abstract
We study the NP-complete Minimum Shared Edges (MSE) problem. Given an undirected graph, a source and a sink vertex, and two integers p and k, the question is whether there are p paths in the graph connecting the source with the sink and sharing at most k edges. Herein, an edge is shared if it appears in at least two paths. We show that MSE is W[1]-hard when parameterized by the treewidth of the input graph and the number k of shared edges combined. We show that MSE is fixed-parameter tractable with respect to p, but does not admit a polynomial-size kernel (unless NP is contained in coNP/poly). In the proof of the fixed-parameter tractability of MSE parameterized by p, we employ the treewidth reduction technique due to Marx, O'Sullivan, and Razgon [ACM TALG 2013].
Cite
@article{arxiv.1602.01739,
title = {The Parameterized Complexity of the Minimum Shared Edges Problem},
author = {Till Fluschnik and Stefan Kratsch and Rolf Niedermeier and Manuel Sorge},
journal= {arXiv preprint arXiv:1602.01739},
year = {2016}
}
Comments
35 pages, 16 figures