### 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 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Discrete Optimization*,

*22*, 111-121. https://doi.org/10.1016/j.disopt.2016.01.003

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

Research output: Contribution to journal › Article

*Discrete Optimization*, vol. 22, pp. 111-121. https://doi.org/10.1016/j.disopt.2016.01.003

}

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 -