On connected domination in unit ball graphs Academic Article uri icon

abstract

  • 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 satisfy the triangle inequality and provide a 3-approximation algorithm for such graphs. We also show that for fixed k the problem is polynomially solvable in unit disk and unit ball graphs. 2010 Springer-Verlag.

published proceedings

  • Optimization Letters

author list (cited authors)

  • Butenko, S., Kahruman-Anderoglu, S., & Ursulenko, O.

citation count

  • 11

complete list of authors

  • Butenko, Sergiy||Kahruman-Anderoglu, Sera||Ursulenko, Oleksii

publication date

  • May 2011