Computational geometry: an introduction
Computational geometry: an introduction
Software—Practice & Experience
How to present a paper on experimental work with algorithms
ACM SIGACT News
Multidimensional divide-and-conquer
Communications of the ACM
Introduction to Algorithms
Divide-and-conquer in multidimensional space
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
An In-Place Sorting with O(n log n) Comparisons and O(n) Moves
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Algorithms in c++, parts 1-4: fundamentals, data structure, sorting, searching, third edition
Algorithms in c++, parts 1-4: fundamentals, data structure, sorting, searching, third edition
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We improve the famous divide-and-conquer algorithm by Bentley and Shamos for the planar closest-pair problem. For n points on the plane, our algorithm keeps the optimal O(n log n) time complexity and, using a circle-packing property, computes at most 7n/2 Euclidean distances, which improves Ge et al.'s bound of (3n log n)/2 Euclidean distances. We present experimental results of our comparative studies on four different versions of the divide-and-conquer closest pair algorithm and propose two effective heuristics.