Fast Hierarchical Clustering and Other Applications of Dynamic Closest Pairs

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 log2 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

• Type: Conference
• Year: 1998
• Where: SODA
• Authors: David Eppstein
• Keywords: Algorithms, Closest Pair, Closest Pair Problems, Data Structures, SODA 1998