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» Piercing Convex Sets
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96
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ISIPTA
1999
IEEE
15 years 4 months ago
Nonlinear Filtering of Convex Sets of Probability Distributions
A solution is provided to the problem of computing a convex set of conditional probability distributions that characterize the state of a nonlinear dynamic system as it evolves in...
John Kenney, Wynn C. Stirling
73
Voted
COMBINATORICA
2008
129views more  COMBINATORICA 2008»
14 years 11 months ago
The combinatorial encoding of disjoint convex sets in the plane
We introduce a new combinatorial object, the double-permutation sequence, and use it to encode a family of mutually disjoint compact convex sets in the plane in a way that capture...
Jacob E. Goodman, Richard Pollack
90
Voted
COMBINATORICS
2004
108views more  COMBINATORICS 2004»
14 years 11 months ago
On the Chromatic Number of Intersection Graphs of Convex Sets in the Plane
Let G be the intersection graph of a finite family of convex sets obtained by translations of a fixed convex set in the plane. We show that every such graph with clique number k i...
Seog-Jin Kim, Alexandr V. Kostochka, Kittikorn Nak...
CORR
2010
Springer
113views Education» more  CORR 2010»
14 years 11 months ago
Opaque sets
The problem of finding "small" sets that meet every straight-line which intersects a given convex region was initiated by Mazurkiewicz in 1916. We call such a set an opa...
Adrian Dumitrescu, János Pach
CCCG
2009
14 years 9 months ago
On symmetric realizations of the simplicial complex of 3-crossing-free sets of diagonals of the octagon
Motivated by the question of the polytopal realizability of the simplicial complex n,k of (k + 1)-crossing-free sets of diagonals of the convex n-gon, we study the first open case...
Jürgen Bokowski, Vincent Pilaud