## A General Approximation Technique For Constrained Forest Problems (1992)

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Venue: | SIAM JOURNAL ON COMPUTING |

Citations: | 347 - 21 self |

### BibTeX

@ARTICLE{Goemans92ageneral,

author = {Michel Goemans and David P. Williamson},

title = {A General Approximation Technique For Constrained Forest Problems},

journal = {SIAM JOURNAL ON COMPUTING},

year = {1992},

volume = {24},

pages = {296--317}

}

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### Abstract

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 fit in this framework, including the shortest path, minimum-cost spanning tree, minimum-weight perfect matching, traveling salesman and Steiner tree problems. Our techniqueproduces approximation algorithms that run in O(n² log n) time and come within a factor of 2 of optimal for most of these problems. For instance, we obtain a 2-approximationalgorithm for the minimum-weight perfect matching problem under the triangle inequality. Our running time of O(n² log n) time compares favorably with the best strongly polynomial exact algorithms running in O(n³) time for dense graphs. A similar result is obtained for the 2-matchingproblem and its variants. We also derive the first approxi...