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DCG
2008
101views more  DCG 2008»
13 years 4 months ago
On the Hardness of Computing Intersection, Union and Minkowski Sum of Polytopes
For polytopes P1, P2 Rd we consider the intersection P1 P2, the convex hull of the union CH(P1 P2), and the Minkowski sum P1 + P2. For Minkowski sum we prove that enumerating t...
Hans Raj Tiwary
COMPGEOM
2007
ACM
13 years 8 months ago
On the hardness of minkowski addition and related operations
For polytopes P, Q Rd we consider the intersection P Q; the convex hull of the union CH(P Q); and the Minkowski sum P + Q. We prove that given rational H-polytopes P1, P2, Q it...
Hans Raj Tiwary
COMPGEOM
2006
ACM
13 years 10 months ago
Colored intersection searching via sparse rectangular matrix multiplication
In a Batched Colored Intersection Searching Problem (CI), one is given a set of n geometric objects (of a certain class). Each object is colored by one of c colors, and the goal i...
Haim Kaplan, Micha Sharir, Elad Verbin
COMPGEOM
2010
ACM
13 years 9 months ago
The 2-center problem in three dimensions
Let P be a set of n points in R3 . The 2-center problem for P is to find two congruent balls of the minimum radius whose union covers P. We present two randomized algorithms for ...
Pankaj K. Agarwal, Rinat Ben Avraham, Micha Sharir
MICS
2010
128views more  MICS 2010»
12 years 11 months ago
Arrangements on Parametric Surfaces II: Concretizations and Applications
We describe the algorithms and implementation details involved in the concretizations of a generic framework that enables exact construction, maintenance, and manipulation of arran...
Eric Berberich, Efi Fogel, Dan Halperin, Michael K...