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» On empty convex polygons in a planar point set
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FOCS
2000
IEEE
15 years 4 months ago
Nearly Optimal Expected-Case Planar Point Location
We consider the planar point location problem from the perspective of expected search time. We are given a planar polygonal subdivision S and for each polygon of the subdivision t...
Sunil Arya, Theocharis Malamatos, David M. Mount
SODA
1996
ACM
121views Algorithms» more  SODA 1996»
15 years 27 days ago
Optimal Placement of Convex Polygons to Maximize Point Containment
Given a convex polygon P with m vertices and a set S of n points in the plane, we consider the problem of nding a placement of P that contains the maximum number of points in S. W...
Matthew Dickerson, Daniel Scharstein
CCCG
2010
15 years 1 months ago
Sweeping minimum perimeter enclosing parallelograms: Optimal crumb cleanup
We examine the problem of pushing all the points of a planar region into one point using parallel sweeps of an infinite line, minimizing the sum of the lengths of the sweep vector...
Yonit Bousany, Mary Leah Karker, Joseph O'Rourke, ...
CORR
2002
Springer
86views Education» more  CORR 2002»
14 years 11 months ago
Small Strictly Convex Quadrilateral Meshes of Point Sets
In this paper we give upper and lower bounds on the number of Steiner points required to construct a strictly convex quadrilateral mesh for a planar point set. In particular, we sh...
David Bremner, Ferran Hurtado, Suneeta Ramaswami, ...
CCCG
2010
15 years 1 months ago
On the variance of random polygons
A random polygon is the convex hull of uniformly distributed random points in a convex body K R2 . General upper bounds are established for the variance of the area of a random p...
William L. Steiger, Imre Bárány