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Helly-Type Theorems in Property Testing
[article]

2013
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arXiv
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pre-print

Helly's theorem is a fundamental result in discrete geometry, describing the ways in which convex sets intersect with each other. If S is a set of n points in R^d, we say that S is (k,G)-clusterable if it can be partitioned into k clusters (subsets) such that each cluster can be contained in a translated copy of a geometric object G. In this paper, as an application of Helly's theorem, by taking a constant size sample from S, we present a testing algorithm for (k,G)-clustering, i.e., to

arXiv:1307.8268v2
fatcat:tgjkwnrz45eppo4ebk73xuqd34