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Efficient Algorithms for the Smallest Enclosing Ball Problem

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Abstract

Consider the problem of computing the smallest enclosing ball of a set of m balls in ℜn. Existing algorithms are known to be inefficient when n > 30. In this paper we develop two algorithms that are particularly suitable for problems where n is large. The first algorithm is based on log-exponential aggregation of the maximum function and reduces the problem into an unconstrained convex program. The second algorithm is based on a second-order cone programming formulation, with special structures taken into consideration. Our computational experiments show that both methods are efficient for large problems, with the product mn on the order of 107. Using the first algorithm, we are able to solve problems with n = 100 and m = 512,000 in about 1 hour.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Curtin University of Technology, Bentley, WA, 6102, Australia

    Guanglu Zhou

  2. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543

    Kim-Chuan Tohemail

  3. Department of Decision Sciences, National University of Singapore, Singapore

    Jie Sun

Authors
  1. Guanglu Zhou
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  2. Kim-Chuan Tohemail
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  3. Jie Sun
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Corresponding author

Correspondence to Guanglu Zhou.

Additional information

His work was supported by Australian Research Council.

Research supported in part by the Singapore-MIT Alliance.

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Zhou, G., Tohemail, KC. & Sun, J. Efficient Algorithms for the Smallest Enclosing Ball Problem. Comput Optim Applic 30, 147–160 (2005). https://doi.org/10.1007/s10589-005-4565-7

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  • DOI: https://doi.org/10.1007/s10589-005-4565-7

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