Approximating minimum-size k-connected spanning subgraphs via matching

Abstract

An efficient heuristic is presented for the problem of finding a minimum-size k-connected spanning subgraph of a given (undirected or directed) graph G=(V,E). There are four versions of the problem, depending on whether G is undirected or directed, and whether the spanning subgraph is required to be k-node connected (k-NCSS) or k-edge connected (k-ECSS). The approximation guarantees are as follows: min-size k-NCSS of an undirected graph 1+[1/k], min-size k-NCSS of a directed graph 1+[1/k], min-size k-ECSS of an undirected graph 1+[7/k], & min-size k-ECSS of a directed graph 1+[4//spl radic/k]. The heuristic is based on a subroutine for the degree-constrained subgraph (b-matching) problem. It is simple, deterministic, and runs in time O(k|E|/sup 2/). For undirected graphs and k=2, a (deterministic) parallel NC version of the heuristic finds a 2-node connected (or a-edge connected) spanning subgraph whose size is within a factor of (1.5+/spl epsiv/) of minimum, where /spl epsiv/>0 is a constant.