The Minimum Generalized Vertex Cover Problem

Let G = (V, E) be an undirected graph, with three numbers d0(e) ≥ d1(e) ≥ d2(e) ≥ 0 for each edge e ∈ E. A solution is a subset U ⊆ V and di(e) represents the cost contributed to the solution by the edge e if exactly i of its endpoints are in the solution. The cost of including a vertex v in the solution is c(v). A solution has cost that is equal to the sum of the vertex costs and the edge costs. The minimum generalized vertex cover problem is to compute a minimum cost set of vertices. We study the complexity of the problem with the costs d0(e) = 1, d1(e) = α and d2(e) = 0 ∀e ∈ E and c(v) = β ∀v ∈ V , for all possible values of α and β. We also provide 2-approximation algorithms for the general case.

• Type: Conference
• Year: 2003
• Where: ESA
• Authors: Refael Hassin, Asaf Levin
• Keywords: Edge, ESA 2003, Minimum Generalized Vertex, Solution