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Random walks on the vertices of transportation polytopes with constant number of sources
 Proc. 14th Ann. ACMSIAM Symp. Disc. Alg. (Baltimore, MD) 330–339, ACM
, 2003
"... We consider the problem of uniformly sampling a vertex of a transportation polytope with m sources and n destinations, where m is a constant. We analyse a natural random walk on the edgevertex graph of the polytope. The analysis makes use of the multicommodity flow technique of Sinclair [30] toget ..."
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Cited by 13 (3 self)
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We consider the problem of uniformly sampling a vertex of a transportation polytope with m sources and n destinations, where m is a constant. We analyse a natural random walk on the edgevertex graph of the polytope. The analysis makes use of the multicommodity flow technique of Sinclair [30] together with ideas developed by Morris and Sinclair [24, 25] for the knapsack problem, and Cryan et al. [3] for contingency tables, to establish that the random walk approaches the uniform distribution in time n O(m2). 1
ON THE GRAPHCONNECTIVITY OF SKELETA OF CONVEX POLYTOPES
, 2008
"... Given a ddimensional convex polytope P and nonnegative integer k not exceeding d − 1, let Gk(P) denote the simple graph on the node set of kdimensional faces of P in which two such faces are adjacent if there exists a (k + 1)dimensional face of P which contains them both. The graph Gk(P) is isom ..."
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Cited by 3 (2 self)
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Given a ddimensional convex polytope P and nonnegative integer k not exceeding d − 1, let Gk(P) denote the simple graph on the node set of kdimensional faces of P in which two such faces are adjacent if there exists a (k + 1)dimensional face of P which contains them both. The graph Gk(P) is isomorphic to the dual graph of the (d − k)dimensional skeleton of the normal fan of P. For fixed values of k and d, the largest integer m such that Gk(P) is mvertexconnected for all ddimensional polytopes P is determined. This result generalizes Balinski’s theorem on the onedimensional skeleton of a ddimensional convex polytope.
Combinatorial Polytope Enumeration
, 2009
"... We describe a provably complete algorithm for the generation of a tight, possibly exact, superset of all combinatorially distinct simple nfacet polytopes in R d, along with their graphs, fvectors, and face lattices. The technique applies repeated cutting planes and planar sweeps to a d−simplex. Ou ..."
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We describe a provably complete algorithm for the generation of a tight, possibly exact, superset of all combinatorially distinct simple nfacet polytopes in R d, along with their graphs, fvectors, and face lattices. The technique applies repeated cutting planes and planar sweeps to a d−simplex. Our generator has implications for several outstanding problems in polytope theory, including conjectures about the number of distinct polytopes, the edge expansion of polytopal graphs, and the dstep conjecture. 1
1 COMPACT HYPERBOLIC COXETER THIN CUBES
, 2014
"... Copyright © 2014 Kalita and Kalita. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract: Andreev’s Theorem provides a complete c ..."
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Copyright © 2014 Kalita and Kalita. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract: Andreev’s Theorem provides a complete characterization of 3dimensional compact hyperbolic combinatorial polytope having nonobtuse dihedral angles. Cube is one of such polytope. In this article, with the help of Andreev’s Theorem, a special type of compact hyperbolic coxeter cube, called thin cube has been studied. Using graph theory and combinatorics, it has been found that there are exactly 3 such cubes in hyperbolic space upto symmetry.
VariableSpeed Linear Morphing
"... The following is a list of the problems presented on August ..."
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Canadian Conference on Computational Geometry held in Halifax, Nova Scotia, Canada.
"... Boxed problem numbers indicate appearance in The ..."
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