Discrete & Computational Geometry

, Volume 34, Issue 1, pp 87-96

First online:

Equipartitions of Measures by 2-Fans

  • Sergey BeregAffiliated withDepartment of Computer Science, University of Texas at Dallas, Box 830688, Richardson, TX 75083 Email author 

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We study the problem of computing an equitable 2-fan for three masses distributed on the 2-sphere. The existence of an equitable 2-fan was shown by Barany and Matousek. The contribution of this paper is twofold. (i) We prove the existence of an infinite set of equitable 2-fans. (ii) We present an efficient algorithm for finding an equitable 2-fan when the mass distributions are discrete, i.e. finite sets of points. Both (i) and (ii) can be easily extended to mass distributions in the plane instead of the sphere.