TY - GEN

T1 - Subexponential fixed-parameter algorithms for partial vector domination

AU - Ishii, Toshimasa

AU - Ono, Hirotaka

AU - Uno, Yushi

N1 - Funding Information:
This work is partially supported by KAKENHI No. 15H00853 , 23500022 , 24700001 , 24106004 , 25104521 , 25106508 , 26280001 and 26540005 , the Kayamori Foundation of Informational Science Advancement and The Asahi Glass Foundation .

PY - 2014

Y1 - 2014

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.

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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

T2 - 3rd International Symposium on Combinatorial Optimization, ISCO 2014

Y2 - 5 March 2014 through 7 March 2014

ER -