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The ACM Journal of Experimental Algorithmics


Volume 5, Article 1, 2000


Fast Hierarchical Clustering and Other Applications of Dynamic Closest Pairs

by

D. Eppstein

http://www.jea.acm.org/2000/EppsteinDynamic/


Abstract:

We develop data structures for dynamic closest pair problems with arbitrary distance functions, that do not necessarily come from any geometric structure on the objects. Based on a technique previously used by the author for Euclidean closest pairs, we show how to insert and delete objects from an n-object set, maintaining the closest pair, in O(n log2n) time per update and O(n) space. With quadratic space, we can instead use a quadtree-like structure to achieve an optimal time bound, O(n) per update. We apply these data structures to hierarchical clustering, greedy matching, and TSP heuristics, and discuss other potential applications in machine learning, Gröbner bases, and local improvement algorithms for partition and placement problems. Experiments show our new methods to be faster in practice than previously used heuristics.

Received
Accepted
Final Revision
Published
December 21, 1999
May 25, 2000
May 30, 2000
June 1, 2000

Last updated and validated June 1, 2000, by editor@jea.acm.org