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Gravitational allocation on the sphere
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DOI：10.1073/pnas.1720804115.png)
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摘要
En 中文
Given a collection L of n points on a sphere S-n(2) of surface area n, a fair allocation is a partition of the sphere into n parts each of area 1, and each is associated with a distinct point of L. We show that, if the n points are chosen uniformly at random and if the partition is defined by a certain gravitational potential, then the expected distance between a point on the sphere and the associated point of L is O(root log n). We use our result to define a matching between two collections of n independent and uniform points on the sphere and prove that the expected distance between a pair of matched points is O(root log n), which is optimal by a result of Ajtai, Komlos, and Tusnady.
Keyword:
bipartite matching
allocation
transportation
gravity
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期刊
P
IF:
9.1
论文数:
10.8W
被引数:
73.5W
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