NC approximation algorithms for 2-connectivity augmentation in a graph

Abstract

Given an undirected graph G = (V, E 0) with |V| = n and a feasible set E of m weighted edges on V, the optimal 2-edge (2-vertex) connectivity augmentation problem is to find a subset S * ⊆ E such that G(V, E 0 ∪ S *) is 2-edge (2-vertex) connected and the weighted sum of edges in S * is minimized. We devise NC approximation algorithms for the optimal 2-edge connectivity and the optimal 2-vertex connectivity augmentation problems by delivering solutions within (1 + ln n c)(1 + ε) times optimum and within (1 + ln n b)(1 + ε) log n b times optimum when G is connected, respectively, where n c is the number of 2-edge connected components of G, nb is the number of biconnected components of G, and ε is a constant with 0 < ε < 1. Consequently, we find an approximation solution for the problem of the minimum 2-edge (biconnected) spanning subgraph on a weighted 2-edge connected (biconnected) graph in the same time and processor bounds.KeywordsMinimum Span TreeArticulation PointSpan SubgraphTree EdgeBiconnected ComponentThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.