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 language | English |
|---|---|
| Pages (from-to) | 111-121 |
| Number of pages | 11 |
| Journal | Discrete Optimization |
| Volume | 22 |
| DOIs | |
| Publication status | Published - Nov 1 2016 |
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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 journal › Article
}
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.
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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 -