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.
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
T2 - 3rd International Symposium on Combinatorial Optimization, ISCO 2014
Y2 - 5 March 2014 through 7 March 2014
ER -