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Engineering the Divide-and-Conquer Closest Pair Algorithm

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Abstract

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.

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Authors and Affiliations

  1. Department of Computer Science, Utah State University, Logan, Utah, 84322-4205, U.S.A.

    Minghui Jiang & Joel Gillespie

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  1. Minghui Jiang
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  2. Joel Gillespie
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Correspondence to Minghui Jiang.

Additional information

This work is partially supported by Utah State University under Grant No. A13501.

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Jiang, M., Gillespie, J. Engineering the Divide-and-Conquer Closest Pair Algorithm. J Comput Sci Technol 22, 532–540 (2007). https://doi.org/10.1007/s11390-007-9066-y

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  • DOI: https://doi.org/10.1007/s11390-007-9066-y

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