Primal-dual based distributed algorithms for vertex cover with semi-hard capacities

In this paper we consider the weighted, capacitated vertex cover problem with hard capacities (capVC). Here, we are given an undirected graph G = (V, E), non-negative vertex weights wtv for all vertices v ∈ V , and node-capacities Bv ≥ 1 for all v ∈ V . A feasible solution to a given capVC instance consists of a vertex cover C ⊆ V . Each edge e ∈ E is assigned to one of its endpoints in C and the number of edges assigned to any vertex v ∈ C is at most Bv. The goal is to minimize the total weight of C. For a parameter > 0 we give a deterministic, distributed algorithm for the capVC problem that computes a vertex cover C of weight at most (2 + ) · opt where opt is the weight of a minimumweight feasible solution to the given instance. The number of edges assigned to any node v ∈ C is at most (4 + ) · Bv. The running time of our algorithm is O(log(nW)/ ), where n is the number of nodes in the network and W = wtmax/wtmin is the ratio of largest to smallest weight. This r...

• Type: Conference
• Year: 2005
• Where: PODC
• Authors: Fabrizio Grandoni, Jochen Könemann, Alessandro Panconesi, Mauro Sozio
• Keywords: Distributed And Parallel Computing, Non-negative Vertex Weights, PODC 2005, Vertex Cover, Vertex Cover Problem