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Cones of matrices and setfunctions and 01 optimization
 SIAM JOURNAL ON OPTIMIZATION
, 1991
"... It has been recognized recently that to represent a polyhedron as the projection of a higher dimensional, but simpler, polyhedron, is a powerful tool in polyhedral combinatorics. We develop a general method to construct higherdimensional polyhedra (or, in some cases, convex sets) whose projection a ..."
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Cited by 347 (7 self)
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It has been recognized recently that to represent a polyhedron as the projection of a higher dimensional, but simpler, polyhedron, is a powerful tool in polyhedral combinatorics. We develop a general method to construct higherdimensional polyhedra (or, in some cases, convex sets) whose projection
Hausdorff Approximation of 3D Convex Polytopes
"... Let P be a convex polytope in R d, d = 3 or 2, with n vertices. We present linear time algorithms for approximating P by simpler polytopes. For instance, one such algorithm selects k < n vertices of P whose convex hull is the approximating polytope. The rate of approximation, in the Hausdorff dis ..."
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Let P be a convex polytope in R d, d = 3 or 2, with n vertices. We present linear time algorithms for approximating P by simpler polytopes. For instance, one such algorithm selects k < n vertices of P whose convex hull is the approximating polytope. The rate of approximation, in the Hausdorff
Binary Positive Semidefinite Matrices and Associated Integer Polytopes
"... We consider the positive semidefinite (psd) matrices with binary entries. We give a characterisation of such matrices, along with a graphical representation. We then move on to consider the associated integer polytopes. Several important and wellknown integer polytopes — the cut, boolean quadric, ..."
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Cited by 3 (0 self)
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, multicut and clique partitioning polytopes — are shown to arise as projections of binary psd polytopes. Finally, we present various valid inequalities for binary psd polytopes, and show how they relate to inequalities known for the simpler polytopes mentioned. Along the way, we answer an open question
Star Unfolding of a Polytope with Applications
 SIAM J. COMPUT
, 1993
"... We define the notion of a star unfolding of the surface P of a convex polytope with n vertices, and use it to solve several problems related to shortest paths on P. The first algorithm computes the edge sequences traversed by shortest paths on P in time O(n 6 fi(n) log n), where fi(n) is an extremel ..."
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Cited by 38 (5 self)
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We define the notion of a star unfolding of the surface P of a convex polytope with n vertices, and use it to solve several problems related to shortest paths on P. The first algorithm computes the edge sequences traversed by shortest paths on P in time O(n 6 fi(n) log n), where fi
Separation in the Polytope Algebra
, 1993
"... . The polytope algebra is the universal group for translation invariant valuations on the family of polytopes in a finite dimensional vector space over an ordered field. In an earlier paper, it was shown that the polytope algebra is, in all but one trivial respect, a graded (commutative) algebra ove ..."
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. The polytope algebra is the universal group for translation invariant valuations on the family of polytopes in a finite dimensional vector space over an ordered field. In an earlier paper, it was shown that the polytope algebra is, in all but one trivial respect, a graded (commutative) algebra
Approximate Polytope Membership Queries
, 2010
"... Convex polytopes are central to computational and combinatorial geometry. In this paper, we consider an approximate version of a fundamental geometric search problem, polytope membership queries. Given a convex polytope P in R d, presented as the intersection of halfspaces, the objective is to prepr ..."
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Cited by 5 (2 self)
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neighbor searching to approximate polytope membership queries. Remarkably, we show that our tradeoff provides significant improvements to the best known spacetime tradeoffs for approximate nearest neighbor searching. Furthermore, this is achieved with constructions that are much simpler than existing
Algorithms for Polytope Covering and Approximation, and for Approximate Closestpoint Queries
, 1993
"... This paper gives an algorithm for polytope covering: let L and U be sets of points in R d , comprising n points altogether. A cover for L from U is a set C ae U with L a subset of the convex hull of C. Suppose c is the size of a smallest such cover, if it exists. The randomized algorithm given he ..."
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Cited by 1 (0 self)
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.[MS92b] A variant algorithm is applied to the problem of approximating the boundary of a polytope with the boundary of a simpler polytope. For an appropriate measure, an approximation with error ffl requires c = O(1=ffl) (d\Gamma1)=2 vertices, and the algorithm gives an approximation with c(5d 3 ln
A Basic Study of the QAPPolytope
 INSTITUT FÜR INFORMATIK, UNIVERSITÄT ZU KÖLN, POHLIGSTRASSE 1, D50969
, 1996
"... We investigate a polytope (the QAPPolytope) beyond a "natural" integer programming formulation of the Quadratic Assignment Problem (QAP) that has been used successfully in order to compute good lower bounds for the QAP in the very recent years. We present basic structural properties of th ..."
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Cited by 5 (0 self)
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of the QAPPolytope, partially independently also obtained by Rijal (1995). The main original contribution of this work is the representation of the QAPPolytope in a space different from the one in which it is defined naturally. This representation provides us with a much simpler way to derive the dimension
On Polytopes Spanned by Sets of Points in R³
, 2001
"... (a) We prove that the total complexity of k polygons in arrangement of n lines with distinct vertices is (nk ). If the polygons do not overlap in edges then we show that their complexity is (nk ) for k n and (n . This bounds are known (see [HS92, Dey98, Epp95]), however we believe t ..."
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that our methods are much simpler. (b) We prove that the maximum total complexity of k polytopes in arrangements of n planes in IR with distinct vertices is O(n ) and ). This bounds are already known (see [AD99]), but again, we use a much simpler technique to prove this results
Constructing neighborly polytopes and oriented matroids
, 2012
"... A dpolytope P is neighborly if every subset of ⌊ d ⌋ vertices is a face of P. In 1982, Shemer introduced 2 a sewing construction that allows to add a vertex to a neighborly polytope in such a way as to obtain a new neighborly polytope. With this, he constructed superexponentially many different n ..."
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Cited by 6 (5 self)
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neighborly polytopes. The concept of neighborliness extends naturally to oriented matroids. Duals of neighborly oriented matroids also have a nice characterization: balanced oriented matroids. In this paper, we generalize Shemer’s sewing construction to oriented matroids, providing a simpler proof. Moreover
Results 1  10
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