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FSTTCS
2004
Springer
14 years 3 months ago
Approximate Range Searching Using Binary Space Partitions
We show how any BSP tree TP for the endpoints of a set of n disjoint segments in the plane can be used to obtain a BSP tree of size O(n · depth(TP )) for the segments themselves, ...
Mark de Berg, Micha Streppel
COMPGEOM
2007
ACM
14 years 2 months ago
An optimal generalization of the centerpoint theorem, and its extensions
We prove an optimal generalization of the centerpoint theorem: given a set P of n points in the plane, there exist two points (not necessarily among input points) that hit all con...
Saurabh Ray, Nabil H. Mustafa
SODA
1992
ACM
109views Algorithms» more  SODA 1992»
13 years 11 months ago
New Algorithms for Minimum Area k-gons
Given a set P of n points in the plane, we wish to find a set Q P of k points for which the convex hull conv(Q) has the minimum area. We solve this, and the related problem of fi...
David Eppstein
MP
2008
99views more  MP 2008»
13 years 10 months ago
Compact formulations as a union of polyhedra
We explore one method for finding the convex hull of certain mixed integer sets. The approach is to break up the original set into a small number of subsets, find a compact polyhed...
Michele Conforti, Laurence A. Wolsey
SODA
1996
ACM
121views Algorithms» more  SODA 1996»
13 years 11 months 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