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JCT
2011
108views more  JCT 2011»
15 years 1 months ago
The number of extreme points of tropical polyhedra
The celebrated upper bound theorem of McMullen determines the maximal number of extreme points of a polyhedron in terms of its dimension and the number of constraints which define...
Xavier Allamigeon, Stéphane Gaubert, Ricard...
COMPGEOM
2009
ACM
16 years 16 days ago
Coresets for polytope distance
Following recent work of Clarkson, we translate the coreset framework to the problems of finding the point closest to the origin inside a polytope, finding the shortest distance...
Bernd Gärtner, Martin Jaggi
179
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DCG
2006
163views more  DCG 2006»
15 years 6 months ago
Isometry-Invariant Valuations on Hyperbolic Space
Abstract. Hyperbolic area is characterized as the unique continuous isometry invariant simple valuation on convex polygons in H2 . We then show that continuous isometry invariant s...
Daniel A. Klain
COMPGEOM
2000
ACM
15 years 10 months ago
Computing approximate shortest paths on convex polytopes
The algorithms for computing a shortest path on a polyhedral surface are slow, complicated, and numerically unstable. We have developed and implemented a robust and efficient algo...
Pankaj K. Agarwal, Sariel Har-Peled, Meetesh Karia
FOCS
2007
IEEE
16 years 11 days ago
On the Hardness and Smoothed Complexity of Quasi-Concave Minimization
In this paper, we resolve the smoothed and approximative complexity of low-rank quasi-concave minimization, providing both upper and lower bounds. As an upper bound, we provide th...
Jonathan A. Kelner, Evdokia Nikolova