Approximating the k-splittable capacitated network design problem

Abstract

We consider the k-splittable capacitated network design problem (kSCND) in a graph G = (V,E) with edge weight w(e) ≥ 0, e â̂̂ E. We are given a vertex s â̂̂ V designated as a sink, a cable capacity λ > 0, and a source set S ⊆ V with demand q(v) ≥ 0, v â̂̂ S. For any edge e â̂̂ E, we are allowed to install an integer number h(e) of copies of e. The kSCND asks to simultaneously send demand q(v) from each source v â̂̂ S along at most k paths to the sink s. A set of such paths can pass through a single copy of an edge in G as long as the total demand along the paths does not exceed the cable capacity λ. The objective is to find a set of paths of G that minimizes the installing cost Σ e â̂̂ E h(e) w(e). In this paper, we propose a -approximation algorithm to the kSCND, where is any approximation ratio achievable for the Steiner tree problem. © 2013 Springer-Verlag Berlin Heidelberg.