Equipartitions of measures by 2-fans

Authors:
Sergey Bereg
Affiliations:
Department of Computer Science, University of Texas at Dallas, Richardson, TX
Venue:
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Year:
2004

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Abstract

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 Bárány and Matoušek [3] The contribution of this paper is two-fold (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.