Abstract

We develop data structures for dynamic closest pair problems with arbitrary (not necessarily geometric) distance functions, 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 log 2 n) 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, Gr obner bases, and local improvement algorithms for partition and placement problems. Experiments show our new methods to be faster in practice than previously used heuristics. 1 Introduction Clustering has long been a mainstay of statistical analysis, and clustering-based methods have attracted attention in other fields: computational biology (reconstruction of evolution...

Citations

5	An introduction to Gröbner bases, (Graduate studies - Adams, Loustaunau - 2003