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COMPGEOM
2009
ACM

Halving lines and measure concentration in the plane

14 years 5 months ago
Halving lines and measure concentration in the plane
Given a set of n points in the plane and a collection of k halving lines of P ℓ1, . . . , ℓk indexed according to the increasing order of their slopes, we denote by d(ℓj, ℓj+1) the number of points in P that lie above ℓj+1 and below ℓj. We prove an upper bound of 3nk1/3 for the sum Pk−1 j=1 d(ℓj, ℓj+1). We show how this problem is related to the halving lines problem and provide several consequences about measure concentration in R2 .
Rom Pinchasi
Added 28 May 2010
Updated 28 May 2010
Type Conference
Year 2009
Where COMPGEOM
Authors Rom Pinchasi
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