Subexponential fixed-parameter algorithms for partial vector domination

Toshimasa Ishii, Hirotaka Ono, Yushi Uno

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

1 Citation (Scopus)

Abstract

Given a graph G = (V, E) of order n and an n-dimensional non-negative vector d = (d(1), d(2),..., d(n)) called demand vector, the vector domination (resp., total vector domination) is the problem of finding a minimum S ⊆ V such that every vertex v in V \ S (resp., in V) has at least d(v) neighbors in S. The (total) vector domination is a generalization of many dominating set type problems, e.g., the dominating set problem, the k-tuple dominating set problem (this k is different from the solution size), and so on, and subexponential fixed-parameter algorithms with respect to solution size for apex-minor-free graphs (so for planar graphs) are known. In this paper, we consider maximization versions of the problems; that is, for a given integer k, the goal is to find an S ⊆ V with size k that maximizes the total sum of satisfied demands. For these problems, we design subexponential fixed-parameter algorithms with respect to k for apex-minor-free graphs.

Original languageEnglish
Title of host publicationCombinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers
PublisherSpringer Verlag
Pages292-304
Number of pages13
ISBN (Print)9783319091730
DOIs
Publication statusPublished - Jan 1 2014
Event3rd International Symposium on Combinatorial Optimization, ISCO 2014 - Lisbon, Portugal
Duration: Mar 5 2014Mar 7 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8596 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other3rd International Symposium on Combinatorial Optimization, ISCO 2014
CountryPortugal
CityLisbon
Period3/5/143/7/14

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Ishii, T., Ono, H., & Uno, Y. (2014). Subexponential fixed-parameter algorithms for partial vector domination. In Combinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers (pp. 292-304). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8596 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-09174-7_25