Proceedings of 37th Conference on Foundations of Computer Science (1996)
Oct. 14, 1996 to Oct. 16, 1996
J. Cheriyan , Dept. of Combinatorics & Optimization, Waterloo Univ., Ont., Canada
R. Thurimella , Dept. of Combinatorics & Optimization, Waterloo Univ., Ont., Canada
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.
graph theory; minimum-size; k-connected spanning subgraphs; matching; k-NCSS; k-ECSS; undirected graphs; heuristic
R. Thurimella and J. Cheriyan, "Approximating minimum-size k-connected spanning subgraphs via matching," Proceedings of 37th Conference on Foundations of Computer Science(FOCS), Burlington, VT, 1996, pp. 292.