TY - GEN

T1 - (Total) vector domination for graphs with bounded branchwidth

AU - Ishii, Toshimasa

AU - Ono, Hirotaka

AU - Uno, Yushi

N1 - Funding Information:
This work is partially supported by KAKENHI Nos. 23500022 , 24700001 , 24106004 , 25104521 , 25106508 and 26280001 , 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 its approximability and inapproximability have been studied under this general framework. In this paper, we show that a (total) vector domination of graphs with bounded branchwidth can be solved in polynomial time. This implies that the problem is polynomially solvable also for graphs with bounded treewidth. Consequently, the (total) vector domination problem for a planar graph is subexponential fixed-parameter tractable with respect to k, where k is the size of solution.

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 its approximability and inapproximability have been studied under this general framework. In this paper, we show that a (total) vector domination of graphs with bounded branchwidth can be solved in polynomial time. This implies that the problem is polynomially solvable also for graphs with bounded treewidth. Consequently, the (total) vector domination problem for a planar graph is subexponential fixed-parameter tractable with respect to k, where k is the size of solution.

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U2 - 10.1007/978-3-642-54423-1_21

DO - 10.1007/978-3-642-54423-1_21

M3 - Conference contribution

AN - SCOPUS:84899994628

SN - 9783642544224

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

SP - 238

EP - 249

BT - LATIN 2014

PB - Springer Verlag

T2 - 11th Latin American Theoretical Informatics Symposium, LATIN 2014

Y2 - 31 March 2014 through 4 April 2014

ER -