Approximating Minimum Power Edge-Multi-Covers

Abstract

Abstract. Given a graph with edge costs, the power of a node is the maximum cost of an edge incident to it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider the following fundamental problem in wireless network design. Given a graph G = (V, E) with edge costs and degree bounds {r(v) : v ∈ V }, the Minimum-Power Edge-Multi-Cover (MPEMC) problem is to find a minimum-power subgraph J of G such that the degree of every node v in J is at least r(v). We give two approximation algorithms for MPEMC, with ratios O(log k) and k + 1/2, where k = maxv∈V r(v) is the maximum degree bound. This improves the previous ratios O(log n) and k + 1, and implies ratios O(log k) for the Minimum-Power k-Outconnected Subgraph and O log k log n n−k for the Minimum-Power k-Connected Subgraph problems; the latter is the currently best known ratio for the min-cost version of the problem.

Minimum shared‐power edge cut

“…In this model, the power at a vertex will be equal to the weight of one of its incident edges, so the possible powers form a discrete set, which makes the problems easier. The literature on power optimization includes approximation algorithms for minimum spanning tree, Steiner forest, k ‐vertex or k ‐edge connected subgraph (all‐pairs, single source, or s ‐ t ), and various degree‐constrained and edge‐cover problems .…”