On connected domination in unit ball graphs

14 years 10 months ago

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Given a simple undirected graph, the minimum connected dominating set problem is to ﬁnd a minimum cardinality subset of vertices D inducing a connected subgraph such that each vertex outside D has at least one neighbor in D. Approximations of minimum connected dominating sets are often used to represent a virtual routing backbone in wireless networks. This paper ﬁrst proposes a constant-ratio approximation algorithm for the minimum connected dominating set problem in unit ball graphs and then introduces and studies the edge-weighted bottleneck connected dominating set problem, which seeks a minimum edge weight in the graph such that the corresponding bottleneck subgraph has a connected dominating set of size k. In wireless network applications this problem can be used to determine an optimal transmission range for a network with a predeﬁned size of the virtual backbone. We show that the problem is hard to approximate within a factor better than 2 in graphs whose edge weights sati...

Sergiy Butenko, Sera Kahruman-Anderoglu, Oleksii U

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