Approximation Algorithms for Prize-Collecting Capacitated Network Design Problems.

In this paper, we study the prize-collecting capacitated network design (PCCND) problem. We have to route the demand of each source to some sinks in a network, or eventually pay the prize to not serving the demand. We need to install multiple cables on the edges of the network to support the service. The goal is to find a feasible solution with the minimum cost. We give a 3.482-approximation algorithm for the PCCND. We also consider a special case of the PCCND, in which there is only one given sink, and present a 2.9672-approximation algorithm.