A 5/4-approximation algorithm for biconnecting a graph with a given Hamiltonian path

Abstract

Finding a minimum size 2-vertex connected spanning subgraph of a k-vertex connected graph G = (V, E) with n vertices and m edges is known to be NP-hard and APX-hard, as well as approximable in O(n2m) time within a factor of 4/3. Interestingly, the problem remains NP-hard even if a Hamiltonian path of G is given as part of the input. For this input-enriched version of the problem, we provide in this paper a linear time and space algorithm which approximates the optimal solution by a factor of no more than min {5/4, 2k-1/2(k-1)}. © Springer-Verlag Berlin Heidelberg 2005.