A general approach to d-dimensional geometric queries
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Equipartitions of Measures by 2-Fans
Discrete & Computational Geometry
Orthogonal ham-sandwich theorem in R3
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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Consider two absolutely continuous probability measures in the plane. A subdivision of the plane into k=2 regions is equitable if every region has weight 1/k in each measure. We show that, for any two probability measures in the plane and any integer k=2, there exists an equitable subdivision of the plane into k regions using at most k-1 horizontal segments and at most k-1 vertical segments. We also prove the existence of orthogonal equipartitions for point measures and present an efficient algorithm for computing an orthogonal equipartition.