TY - GEN
T1 - Maximum Domination problem
AU - Miyano, Eiji
AU - Ono, Hirotaka
PY - 2011/12/1
Y1 - 2011/12/1
N2 - We consider new variants of the vertex/edge domination problems on graphs. A vertex is said to dominate itself and its all adjacent vertices, and similarly an edge is said to dominate itself and its all adjacent edges. Given an input graph G = (V;E) and an integer k, the κ-Vertex (κ-Edge) Maximum Domination (κ-MaxVD and κ-MaxED, respectively) is to find a subset D V ⊆ V of vertices (resp., D E ⊆ E of edges) with size at most k that maximizes the cardinality of dominated vertices (resp., edges). In this paper, we first show that a simple greedy strategy achieves an approximation ratio of (1 - 1=e) for both k-MaxVD and κ-MaxED. Then, we show that this approximation ratio is the best possible for κ-MaxVD unless P = NP. We also prove that, for any constant ε > 0, there is no polynomial time 1303=1304+ε approximation algorithm for κ-MaxED unless P = NP. However, if k is not larger than the size of the minimum maximal matching, κ-MaxED is 3/4-approximable in polynomial time.
AB - We consider new variants of the vertex/edge domination problems on graphs. A vertex is said to dominate itself and its all adjacent vertices, and similarly an edge is said to dominate itself and its all adjacent edges. Given an input graph G = (V;E) and an integer k, the κ-Vertex (κ-Edge) Maximum Domination (κ-MaxVD and κ-MaxED, respectively) is to find a subset D V ⊆ V of vertices (resp., D E ⊆ E of edges) with size at most k that maximizes the cardinality of dominated vertices (resp., edges). In this paper, we first show that a simple greedy strategy achieves an approximation ratio of (1 - 1=e) for both k-MaxVD and κ-MaxED. Then, we show that this approximation ratio is the best possible for κ-MaxVD unless P = NP. We also prove that, for any constant ε > 0, there is no polynomial time 1303=1304+ε approximation algorithm for κ-MaxED unless P = NP. However, if k is not larger than the size of the minimum maximal matching, κ-MaxED is 3/4-approximable in polynomial time.
UR - http://www.scopus.com/inward/record.url?scp=84864629153&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84864629153&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:84864629153
SN - 9781920682989
T3 - Conferences in Research and Practice in Information Technology Series
SP - 55
EP - 61
BT - Theory of Computing 2011 - Proceedings of the 17th Computing
T2 - Theory of Computing 2011 - 17th Computing: The Australasian Theory Symposium, CATS 2011
Y2 - 17 January 2011 through 20 January 2011
ER -