Approximating minimum-power edge-covers and 2, 3-connectivity

Given a graph with edge costs, the power of a node is the maximum cost of an edge leaving it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider several fundamental undirected network design problems under the power minimization criteria. The Minimum-Power Edge-Cover (MPEC) problem is: given a graph G = (V, E) with edge costs {c(e) : e ∈ E} and a subset S ⊆ V of nodes, find a minimum-power subgraph H of G containing an edge incident to every node in S. We give a 3/2-approximation algorithm for MPEC, improving over the 2-approximation by [11]. For the Min-Power k-Connected Subgraph (MPk-CS) problem we obtain the following results. For k = 2 and k = 3, we improve the best previously known ratios of 4 [3] and 7 [11] to 3 2 3 and 5 2 3 , respectively. Finally, we give a 4rmax-approximation algorithm for the Minimum-Power Steiner Network (MPSN) problem: find a minimum-power subgraph that contains r(u, v) pairwise edgedisjoint paths for every pair u, v of nodes.