Parameterized complexity classification of deletion to list matrix-partition for low-order matrices

Akanksha Agrawal, Sudeshna Kolay, Jayakrishnan Madathil, Saket Saurabh

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

Abstract

Given a symmetric ` × ` matrix M = (mi,j) with entries in {0, 1, ∗}, a graph G and a function L : V (G) → 2[`] (where [`] = {1, 2, . . ., `}), a list M-partition of G with respect to L is a partition of V (G) into ` parts, say, V1, V2, . . ., V` such that for each i, j ∈ {1, 2, . . ., `}, (i) if mi,j = 0 then for any u ∈ Vi and v ∈ Vj, uv ∈/ E(G), (ii) if mi,j = 1 then for any (distinct) u ∈ Vi and v ∈ Vj, uv ∈ E(G), (iii) for each v ∈ V (G), if v ∈ Vi then i ∈ L(v). We consider the Deletion to List M-Partition problem that takes as input a graph G, a list function L : V (G) → 2[`] and a positive integer k. The aim is to determine whether there is a k-sized set S ⊆ V (G) such that G − S has a list M-partition. Many important problems like Vertex Cover, Odd Cycle Transversal, Split Vertex Deletion, Multiway Cut and Deletion to List Homomorphism are special cases of the Deletion to List M-Partition problem. In this paper, we provide a classification of the parameterized complexity of Deletion to List M-Partition, parameterized by k, (a) when M is of order at most 3, and (b) when M is of order 4 with all diagonal entries belonging to {0, 1}.

Original languageEnglish
Title of host publication30th International Symposium on Algorithms and Computation, ISAAC 2019
EditorsPinyan Lu, Guochuan Zhang
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771306
DOIs
StatePublished - 1 Dec 2019
Event30th International Symposium on Algorithms and Computation, ISAAC 2019 - Shanghai, China
Duration: 8 Dec 201911 Dec 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume149
ISSN (Print)1868-8969

Conference

Conference30th International Symposium on Algorithms and Computation, ISAAC 2019
Country/TerritoryChina
CityShanghai
Period8/12/1911/12/19

Keywords

  • Almost 2-SAT
  • Important separators
  • Iterative compression
  • List matrix partitions
  • Parameterized classification

ASJC Scopus subject areas

  • Software

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