A Primal-Dual Approximation Algorithm for Partial Vertex Cover: Making Educated Guesses

We study the partial vertex cover problem. Given a graph G = (V, E), a weight function w : V → R+ , and an integer s, our goal is to cover all but s edges, by picking a set of vertices with minimum weight. The problem is clearly NP-hard as it generalizes the well-known vertex cover problem. We provide a primal-dual 2-approximation algorithm which runs in O(n log n+m) time. This represents an improvement in running time from the previously known fastest algorithm. Our technique can also be used to get a 2-approximation for a more general version of the problem. In the partial capacitated vertex cover problem each vertex u comes with a capacity ku. A solution consists of a function x : V → N0 and an orientation of all but s edges, such that the number of edges oriented toward vertex u is at most xuku. Our objective is to find a cover that minimizes v∈V xvwv. This is the first 2-approximation for the problem and also runs in O(n log n + m) time. ∗ Research supported by NSF Awar...

• Type: Conference
• Year: 2005
• Where: APPROX
• Authors: Julián Mestre
• Keywords: Algorithms, APPROX 2005, Partial Vertex Cover, Vertex Cover Problem, Well-known Vertex Cover