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COMGEO
1998
ACM
13 years 5 months ago
The union of moving polygonal pseudodiscs - Combinatorial bounds and applications
Let P be a set of polygonal pseudodiscs in the plane with n edges in total translating with xed velocities in xed directions. We prove that the maximumnumber of combinatorial chan...
Mark de Berg, Hazel Everett, Leonidas J. Guibas
CORR
2007
Springer
118views Education» more  CORR 2007»
13 years 4 months ago
Contains and Inside relationships within combinatorial Pyramids
7 Irregular pyramids are made of a stack of successively reduced graphs embedded in the plane. Such pyramids are used within the segmentation framework to encode a hierarchy of pa...
Luc Brun, Walter G. Kropatsch
FSTTCS
2004
Springer
13 years 10 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
ORDER
2006
154views more  ORDER 2006»
13 years 5 months ago
A Bipartite Analogue of Dilworth's Theorem
Let r be a fixed positive integer. It is shown that, given any partial orders >1, . . ., >r on the same n-element set P, there exist disjoint subsets A, B P, each with at l...
Jacob Fox
COMPGEOM
2006
ACM
13 years 11 months ago
An optimal-time algorithm for shortest paths on a convex polytope in three dimensions
We present an optimal-time algorithm for computing (an implicit representation of) the shortest-path map from a fixed source s on the surface of a convex polytope P in three dime...
Yevgeny Schreiber, Micha Sharir