A General Approximation Technique for Constrained Forest Problems

We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles or paths satisfying certain requirements. In particular, many basic combinatorial optimization problems t in this framework, including the shortest path, minimum-cost spanning tree, minimum-weight perfect matching, traveling salesman and Steiner tree problems. Our techniqueproducesapproximationalgorithmsthatrunin O(n2 logn) timeandcomewithina factorof 2 of optimalfor mostoftheseproblems. For instance,we obtaina2-approximationalgorithm for the minimum-weightperfectmatchingproblemunderthe triangleinequality. Our runningtime of O(n2 logn) time compares favorably with the best strongly polynomial exact algorithms running in O(n3) timefor dense graphs. A similarresultis obtainedfor the 2-matchingproblemand its variants. We alsoderivethe rstapproximationalgorithmsformanyNP-completeproblems,including...

• Type: Conference
• Year: 1992
• Where: SODA
• Authors: Michel X. Goemans, David P. Williamson
• Keywords: Algorithms, Combinatorial Optimization Problems, SODA 1992, Steiner Tree Problem, Traveling Salesman