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 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 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 کاملDynamic ham-sandwich cuts in the plane
We design efficient data structures for dynamically maintaining a ham-sandwich cut of two point sets in the plane subject to insertions and deletions of points in either set. A hamsandwich cut is a line that simultaneously bisects the cardinality of both point sets. For general point sets, our first data structure supports each operation in O(n) amortized time and O(n) space. Our second data st...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2007
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-006-1287-2