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Minimizing the Number of Separating Circles for Two Sets of Points in the Plane

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5 Author(s)
Jiaye Wang ; Dept. of Comput. Sci., Shandong Econimical Univ., Jinan, China ; Feng Sun ; Wenping Wang ; Chunyan Miao
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Given two sets of points ℝ and B in the plane, we address the problem of finding a set of circles ℂ = {ci, i = 1, 2,... ,k}, satisfying the condition that every point in ℝ is covered by at least one circle in ℂ and each point in B is not covered by any circle in ℂ. We conjecture that to find such a set with the smallest k is NP-hard. In this paper, we present an approximation algorithm for computing the set with minimal number of such circles. The algorithm finds also a lower bound of the smallest k.

Published in:

Voronoi Diagrams in Science and Engineering (ISVD), 2011 Eighth International Symposium on

Date of Conference:

28-30 June 2011