eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-05
106:1
106:20
10.4230/LIPIcs.ICALP.2023.106
article
Tight Bounds for Chordal/Interval Vertex Deletion Parameterized by Treewidth
Włodarczyk, Michał
1
https://orcid.org/0000-0003-0968-8414
Ben-Gurion University, Beer Sheva, Israel
In Chordal/Interval Vertex Deletion we ask how many vertices one needs to remove from a graph to make it chordal (respectively: interval). We study these problems under the parameterization by treewidth tw of the input graph G. On the one hand, we present an algorithm for Chordal Vertex Deletion with running time 2^𝒪(tw)⋅|V(G)|, improving upon the running time 2^𝒪(tw²)⋅|V(G)|^𝒪(1) by Jansen, de Kroon, and Włodarczyk (STOC'21). When a tree decomposition of width tw is given, then the base of the exponent equals 2^{ω-1}⋅3 + 1. Our algorithm is based on a novel link between chordal graphs and graphic matroids, which allows us to employ the framework of representative families. On the other hand, we prove that the known 2^𝒪(tw log tw)⋅|V(G)|-time algorithm for Interval Vertex Deletion cannot be improved assuming Exponential Time Hypothesis.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol261-icalp2023/LIPIcs.ICALP.2023.106/LIPIcs.ICALP.2023.106.pdf
fixed-parameter tractability
treewidth
chordal graphs
interval graphs
matroids
representative families