TY - JOUR

T1 - Subexponential fixed-parameter algorithms for partial vector domination

AU - Ishii, Toshimasa

AU - Ono, Hirotaka

AU - Uno, Yushi

N1 - Publisher Copyright:
© 2016 Elsevier B.V.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

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.

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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 -