### 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 language | English |
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Title of host publication | Combinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers |

Publisher | Springer Verlag |

Pages | 292-304 |

Number of pages | 13 |

ISBN (Print) | 9783319091730 |

DOIs | |

Publication status | Published - Jan 1 2014 |

Event | 3rd International Symposium on Combinatorial Optimization, ISCO 2014 - Lisbon, Portugal Duration: Mar 5 2014 → Mar 7 2014 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8596 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd International Symposium on Combinatorial Optimization, ISCO 2014 |
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Country | Portugal |

City | Lisbon |

Period | 3/5/14 → 3/7/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Subexponential fixed-parameter algorithms for partial vector domination

AU - Ishii, Toshimasa

AU - Ono, Hirotaka

AU - Uno, Yushi

PY - 2014/1/1

Y1 - 2014/1/1

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 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.

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 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.

UR - http://www.scopus.com/inward/record.url?scp=84905854052&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84905854052&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-09174-7_25

DO - 10.1007/978-3-319-09174-7_25

M3 - Conference contribution

AN - SCOPUS:84905854052

SN - 9783319091730

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 292

EP - 304

BT - Combinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers

PB - Springer Verlag

ER -