Approximating Minimum-Size k-Connected Spanning Subgraphs via Matching

Abstract An e cient heuristic is presented for the problem of nding a minimum size k connected spanning subgraph of an undirected or directed simple graph G V E There are four versions of the problem and the approximation guarantees are as followsAn e cient heuristic is presented for the problem of nding a minimum size k connected spanning subgraph of an undirected or directed simple graph G V E There are four versions of the problem and the approximation guarantees are as follows minimum size k node connected spanning subgraph of an undirected graph k minimum size k node connected spanning subgraph of a directed graph k minimum size k edge connected spanning subgraph of an undirected graph k and minimum size k edge connected spanning subgraph of a directed graph p k The heuristic is based on a subroutine for the degree constrained subgraph b matching prob lem It is simple deterministic and runs in time O kjEj The analyses of the heuristics for minimum size k node connected spanning subgraphs hinge on theorems of Mader For undirected graphs and k a deterministic parallelNC version of the heuristic nds a node connected or edge connected spanning subgraph whose size is within a factor of of minimum where is a constant