Subexponential fixed-parameter algorithms for partial vector domination

Toshimasa Ishii, Hirotaka Ono, Yushi Uno

Research output: Contribution to journalArticle

2 Citations (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 (total) dominating set problem, the (total) k-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
Pages (from-to)111-121
Number of pages11
JournalDiscrete Optimization
Volume22
DOIs
Publication statusPublished - Nov 1 2016

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
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

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

In: Discrete Optimization, Vol. 22, 01.11.2016, p. 111-121.

Research output: Contribution to journalArticle

Ishii, Toshimasa ; Ono, Hirotaka ; Uno, Yushi. / Subexponential fixed-parameter algorithms for partial vector domination. In: Discrete Optimization. 2016 ; Vol. 22. pp. 111-121.
@article{6194c8cad0ed439eb1f49d0c68c7a63b,
title = "Subexponential fixed-parameter algorithms for partial vector domination",
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 (total) dominating set problem, the (total) k-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.",
author = "Toshimasa Ishii and Hirotaka Ono and Yushi Uno",
year = "2016",
month = "11",
day = "1",
doi = "10.1016/j.disopt.2016.01.003",
language = "English",
volume = "22",
pages = "111--121",
journal = "Discrete Optimization",
issn = "1572-5286",
publisher = "Elsevier",

}

TY - JOUR

T1 - Subexponential fixed-parameter algorithms for partial vector domination

AU - Ishii, Toshimasa

AU - Ono, Hirotaka

AU - Uno, Yushi

PY - 2016/11/1

Y1 - 2016/11/1

N2 - 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 (total) dominating set problem, the (total) k-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.

AB - 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 (total) dominating set problem, the (total) k-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.

UR - http://www.scopus.com/inward/record.url?scp=84956856571&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84956856571&partnerID=8YFLogxK

U2 - 10.1016/j.disopt.2016.01.003

DO - 10.1016/j.disopt.2016.01.003

M3 - Article

AN - SCOPUS:84956856571

VL - 22

SP - 111

EP - 121

JO - Discrete Optimization

JF - Discrete Optimization

SN - 1572-5286

ER -