A faster implementation of the Goemans-Williamson clustering algorithm

Authors:
Richard Cole;Ramesh Hariharan;Moshe Lewenstein;Ely Porat
Affiliations:
Courant Institute, NYU, New York;Indian Institute of Science, Bangalore;Bar-Ilan University, Ramat Gan, and Courant Institute, NYU, New York;Bar-Ilan University, Ramat Gan
Venue:
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Year:
2001

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Abstract

We give an implementation of the Goemans-Williamson clustering procedure which is at the core of several approximation algorithms including those for Generalized Steiner Trees, Prize Collecting Travelling Salesman, 2-Edge Connected Subgraph etc. On a graph with n nodes and m edge, our implementation gives &Ogr; (k(n + m) log2 n) time approximation algorithms for all these problems at the expense of a slight additive degradation of 1/nk in the approximation factor, for any constant k.