Randomized Data Structures for the Dynamic Closest-Pair Problem

We describe a new randomized data structure, the sparse partition, for solving the dynamic closest-pair problem. Using this data structure the closest pair of a set of n points in D-dimensional space, for any fixed D, can be found in constant time. If a frame containing all the points is known in advance, and if the floor function is available at unit cost, then the data structure supports insertions into and deletions from the set in expected O(log n) time and requires expected O(n) space. This method is more efficient than any deterministic algorithm for solving the problem in

• Type: Journal
• Year: 1998
• Where: SIAMCOMP
• Authors: Mordecai J. Golin, Rajeev Raman, Christian Schwarz, Michiel H. M. Smid
• Keywords: Data Structure, Dynamic Closest-pair Problem, SIAMCOMP 1998, Sparse Partition