eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
28:1
28:18
10.4230/LIPIcs.IPEC.2023.28
article
On the Parameterized Complexity of Multiway Near-Separator
Jansen, Bart M. P.
1
https://orcid.org/0000-0001-8204-1268
Roy, Shivesh K.
1
https://orcid.org/0000-0003-0896-3437
Eindhoven University of Technology, The Netherlands
We study a new graph separation problem called Multiway Near-Separator. Given an undirected graph G, integer k, and terminal set T ⊆ V(G), it asks whether there is a vertex set S ⊆ V(G) ⧵ T of size at most k such that in graph G-S, no pair of distinct terminals can be connected by two pairwise internally vertex-disjoint paths. Hence each terminal pair can be separated in G-S by removing at most one vertex. The problem is therefore a generalization of (Node) Multiway Cut, which asks for a vertex set for which each terminal is in a different component of G-S. We develop a fixed-parameter tractable algorithm for Multiway Near-Separator running in time 2^{𝒪(k log k)} ⋅ n^{𝒪(1)}. Our algorithm is based on a new pushing lemma for solutions with respect to important separators, along with two problem-specific ingredients. The first is a polynomial-time subroutine to reduce the number of terminals in the instance to a polynomial in the solution size k plus the size of a given suboptimal solution. The second is a polynomial-time algorithm that, given a graph G and terminal set T ⊆ V(G) along with a single vertex x ∈ V(G) that forms a multiway near-separator, computes a 14-approximation for the problem of finding a multiway near-separator not containing x.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.28/LIPIcs.IPEC.2023.28.pdf
fixed-parameter tractability
multiway cut
near-separator