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» Lower bounds for expected-case planar point location
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COMGEO
2004
ACM
13 years 5 months ago
A lower bound on the number of triangulations of planar point sets
We show that the number of straight-edge triangulations exhibited by any set of n points in general position in the plane is bounded from below by (2.33n). 2004 Elsevier B.V. All ...
Oswin Aichholzer, Ferran Hurtado, Marc Noy
COMGEO
2007
ACM
13 years 5 months ago
Geometric dilation of closed planar curves: New lower bounds
Given two points on a closed planar curve, C, we can divide the length of a shortest connecting path in C by their Euclidean distance. The supremum of these ratios, taken over all...
Annette Ebbers-Baumann, Ansgar Grüne, Rolf Kl...
WADS
2005
Springer
95views Algorithms» more  WADS 2005»
13 years 11 months ago
Improved Approximation Bounds for Planar Point Pattern Matching
We analyze the performance of simple algorithms for matching two planar point sets under rigid transformations so as to minimize the directed Hausdorff distance between the sets....
Minkyoung Cho, David M. Mount
SIAMCOMP
1998
138views more  SIAMCOMP 1998»
13 years 5 months ago
Dynamic Trees and Dynamic Point Location
This paper describes new methods for maintaining a point-location data structure for a dynamically changing monotone subdivision S. The main approach is based on the maintenance of...
Michael T. Goodrich, Roberto Tamassia
ESA
2004
Springer
160views Algorithms» more  ESA 2004»
13 years 11 months ago
Optimal External Memory Planar Point Enclosure
Abstract. In this paper we study the external memory planar point enclosure problem: Given N axis-parallel rectangles in the plane, construct a data structure on disk (an index) su...
Lars Arge, Vasilis Samoladas, Ke Yi