Complexity of most vital nodes for independent set in graphs related to tree structures

Cristina Bazgan, Sonia Toubaline, Zsolt Tuza

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

Given an undirected graph with weights on its vertices, the k most vital nodes independent set problem consists of determining a set of k vertices whose removal results in the greatest decrease in the maximum weight of independent sets. We also consider the complementary problem, minimum node blocker independent set that consists of removing a subset of vertices of minimum size such that the maximum weight of independent sets in the remaining graph is at most a specified value. We show that these problems are NP-hard on bipartite graphs but polynomial-time solvable on unweighted bipartite graphs. Furthermore, these problems are polynomial also on graphs of bounded treewidth and cographs. A result on the non-existence of a ptas is presented, too.

Original languageEnglish
Title of host publicationCombinatorial Algorithms - 21st International Workshop, IWOCA 2010, Revised Selected Papers
PublisherSpringer Verlag
Pages154-166
Number of pages13
ISBN (Print)9783642192210
DOIs
Publication statusPublished - Jan 1 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6460 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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Keywords

  • NP-hard
  • bipartite graph
  • bounded treewidth
  • cograph
  • complexity
  • independent set
  • most vital nodes
  • ptas

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Bazgan, C., Toubaline, S., & Tuza, Z. (2011). Complexity of most vital nodes for independent set in graphs related to tree structures. In Combinatorial Algorithms - 21st International Workshop, IWOCA 2010, Revised Selected Papers (pp. 154-166). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6460 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-19222-7_17