Kernels for the Disjoint Paths Problem on Subclasses of Chordal Graphs

Juhi Chaudhary, Harmender Gahlawat, Michal Włodarczyk, Meirav Zehavi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Given an undirected graph G and a multiset of k terminal pairs X, the Vertex-Disjoint Paths (VDP) and Edge-Disjoint Paths (EDP) problems ask whether G has k pairwise internally vertexdisjoint paths and k pairwise edge-disjoint paths, respectively, connecting every terminal pair in X. In this paper, we study the kernelization complexity of VDP and EDP on subclasses of chordal graphs. For VDP, we design a 4k vertex kernel on split graphs and an O(k2) vertex kernel on well-partitioned chordal graphs. We also show that the problem becomes polynomial-time solvable on threshold graphs. For EDP, we first prove that the problem is NP-complete on complete graphs. Then, we design an O(k2.75) vertex kernel for EDP on split graphs, and improve it to a 7k+1 vertex kernel on threshold graphs. Lastly, we provide an O(k2) vertex kernel for EDP on block graphs and a 2k + 1 vertex kernel for clique paths. Our contributions improve upon several results in the literature, as well as resolve an open question by Heggernes et al.

Original languageAmerican English
Title of host publication18th International Symposium on Parameterized and Exact Computation, IPEC 2023
EditorsNeeldhara Misra, Magnus Wahlstrom
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959773058
DOIs
StatePublished - 1 Dec 2023
Event18th International Symposium on Parameterized and Exact Computation, IPEC 2023 - Amsterdam, Netherlands
Duration: 6 Sep 20238 Sep 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume285

Conference

Conference18th International Symposium on Parameterized and Exact Computation, IPEC 2023
Country/TerritoryNetherlands
CityAmsterdam
Period6/09/238/09/23

Keywords

  • Edge-Disjoint Paths Problem
  • Kernelization
  • Parameterized Complexity
  • Vertex-Disjoint Paths Problem

All Science Journal Classification (ASJC) codes

  • Software

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