منابع مشابه
Generalized Ham-Sandwich Cuts
Bárány, Hubard, and Jerónimo recently showed that for given wellseparated convex bodies S1, . . . , Sd in R and constants βi ∈ [0,1], there exists a unique hyperplane h with the property that Vol(h+ ∩ Si) = βi · Vol(Si); h+ is the closed positive transversal halfspace of h, and h is a “generalized ham-sandwich cut.” We give a discrete analogue for a set S of n points in R which are partitioned ...
متن کاملComputing generalized ham-sandwich cuts
Article history: Received 24 August 2011 Received in revised form 11 March 2012 Accepted 15 March 2012 Available online 19 March 2012 Communicated by F.Y.L. Chin
متن کاملWeighted Ham-Sandwich Cuts
Let R and B be two sets of n points. A ham-sandwich cut is a line that simultaneously bisects R and B, and is known to always exist. This notion can be generalized to the case where each point p ∈ R ∪ B is associated with a weight wp. A ham-sandwich cut can still be proved to exist, even if weights are allowed to be negative. In this paper, we present a O(n logn) algorithm to find a weighted ha...
متن کاملAlgorithms for Ham Sandwich Cuts
Given disjoint sets PI, P2 ..... Pd in R a with n points in total, a ham-sandwich cut is a hyperplane that simultaneously bisects the Pi. We present algorithms for finding ham-sandwich cuts in every dimension d > 1. When d = 2, the algorithm is optimal, having complexity O(n). For dimension d > 2, the bound on the running time is proportional to the worst-case time needed for constructing a lev...
متن کاملGeneralized Ham-Sandwich Cuts for Well Separated Point Sets
Bárány, Hubard, and Jerónimo recently showed that for given well separated convex bodies S1, . . . , Sd in R and constants βi ∈ [0, 1], there exists a unique hyperplane h with the property that Vol(h ∩Si) = βi·Vol(Si); h is the closed positive transversal halfspace of h, and h is a “generalized ham-sandwich cut”. We give a discrete analogue for a set S of n points in R which is partitioned into...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2009
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-009-9225-8