Approximating node connectivity problems via set covers

Given a graph (directed or undirected) with costs on the edges, and an integer k, we consider the problem of nding a k-node connected spanning subgraph of minimum cost. For the general instance of the problem (directed or undirected), there is a simple 2k-approximation algorithm. Better algorithms are known for various ranges of n; k. For undirected graphs with metric costs Khuller and Raghavachari gave a 2 + 2(k 1) n approximation algorithm. We obtain the following results. (i) For arbitrary costs, a k-approximation algorithm for undirected graphs and a (k + 1)-approximation algorithm for directed graphs. (ii) For metric costs, a (2+ k 1 n )-approximation algorithm for undirected graphs and a (2 + k n )-approximation algorithm for directed graphs. For undirected graphs and k = 6; 7, we further improve the approximation ratio from k to d(k + 1)=2e = 4; previously, d(k + 1)=2e-approximation algorithms were known only for k 5. We also give a fast 3-approximation algorithm for k = 4. The...

• Type: Conference
• Year: 2000
• Where: APPROX
• Authors: Guy Kortsarz, Zeev Nutov
• Keywords: Algorithm, Algorithms, APPROX 2000, Metric Costs, Undirected Graphs