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

Fingerprint

Fixed-parameter Algorithms
Domination
Partial
Dominating Set
Apex
Minor
Graph in graph theory
Planar graph
n-dimensional
Maximise
Non-negative
Integer
Vertex of a graph

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

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

Subexponential fixed-parameter algorithms for partial vector domination. / Ishii, Toshimasa; Ono, Hirotaka; Uno, Yushi.

Combinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers. Springer Verlag, 2014. p. 292-304 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8596 LNCS).

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

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. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8596 LNCS, Springer Verlag, pp. 292-304, 3rd International Symposium on Combinatorial Optimization, ISCO 2014, Lisbon, Portugal, 3/5/14. https://doi.org/10.1007/978-3-319-09174-7_25
Ishii T, Ono H, Uno Y. Subexponential fixed-parameter algorithms for partial vector domination. In Combinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers. Springer Verlag. 2014. p. 292-304. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-09174-7_25
Ishii, Toshimasa ; Ono, Hirotaka ; Uno, Yushi. / Subexponential fixed-parameter algorithms for partial vector domination. Combinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers. Springer Verlag, 2014. pp. 292-304 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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