Approximation of Partial Capacitated Vertex Cover

We study the partial capacitated vertex cover problem (pcvc) in which the input consists of a graph G and a covering requirement L. Each edge e in G is associated with a demand (or load) ℓ(e), and each vertex v is associated with a (soft) capacity c(v) and a weight w(v). A feasible solution is an assignment of edges to vertices such that the total demand of assigned edges is at least L. The weight of a solution is v α(v)w(v), where α(v) is the number of copies of v required to cover the demand of the edges that are assigned to v. The goal is to find a solution of minimum weight. We consider three variants of pcvc. In pcvc with separable demands the only requirement is that total demand of edges assigned to v is at most α(v)c(v). In pcvc with inseparable demands there is an additional requirement that if an edge is assigned to v then it must be assigned to one of its copies. The third variant is the unit demands version. We present 3-approximation algorithms for both pcvc with se...

• Type: Conference
• Year: 2007
• Where: ESA
• Authors: Reuven Bar-Yehuda, Guy Flysher, Julián Mestre, Dror Rawitz
• Keywords: Capacitated Vertex Cover, ESA 2007, Inseparable Demands, Separable Demands