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- Komei Fukuda, Christophe Weibel
- Discrete & Computational Geometry
- 2007

The objective of this paper is to present two types of results on Minkowski sums of convex polytopes. The first is about a special class of polytopes called perfectly centered and the combinatorial properties of the Minkowski sum with their own dual. In particular, we have a characterization of faces of the sum in terms of the face lattice of a given… (More)

- Efi Fogel, Dan Halperin, Christophe Weibel
- Discrete & Computational Geometry
- 2009

We present a tight bound on the exact maximum complexity of Minkowski sums of poly-topes in R 3. In particular, we prove that the maximum number of facets of the Minkowski sum of k polytopes with m

The objective of this paper is to present two types of results on Minkowski sums of convex polytopes. The first is about a special class of polytopes we call perfectly centered and the combinatorial properties of the Minkowski sum with their own dual. In particular, we have a characterization of face lattice of the sum in terms of the face lattice of a… (More)

- Christophe Weibel
- Discrete & Computational Geometry
- 2012

It is known that in the Minkowski sum of r polytopes in dimension d, with r < d, the number of vertices of the sum can potentially be as high as the product of the number of vertices in each summand [2]. However, the number of vertices for sums of more polytopes was unknown so far. In this paper, we study sums of polytopes in general orientations, and show… (More)

Consider a <i>routing problem</i> instance consisting of a <i>demand graph H</i> = (<i>V, E</i>(<i>H</i>)) and a <i>supply graph G</i> = (<i>V, E</i>(<i>G</i>)). If the pair obeys the cut condition, then the <i>flow-cut gap</i> for this instance is the minimum value <i>C</i> such that there exists a feasible multiflow for <i>H</i> if each edge of <i>G</i>… (More)

- Amit Chakrabarti, Lisa Fleischer, Christophe Weibel
- STOC
- 2012

Let G=(V,E) be a supply graph and H=(V,F) a demand graph defined on the same set of vertices. An assignment of capacities to the edges of G and demands to the edges of H is said to satisfy the <i>cut condition</i> if for any cut in the graph, the total demand crossing the cut is no more than the total capacity crossing it. The pair (G,H) is called… (More)

Contents Abstract 7 Résumé 9

The 3D visibility skeleton is a data structure used to encode global visibility information about a set of objects. Previous theoretical results have shown that for k convex polytopes with n edges in total, the worst case size complexity of this data structure is Θ(n 2 k 2) [Brönnimann et al. 07]; whereas for k uniformly distributed unit spheres, the… (More)

- Efi Fogel, Dan Halperin, Christophe Weibel
- Symposium on Computational Geometry
- 2007

We present a tight bound on the exact maximum complexity of Minkowski sums of convex polyhedra in R 3. In particular , we prove that the maximum number of facets of the Minkowski sum of two convex polyhedra with m and n facets respectively is bounded from above by f (m, n) = 4mn−9m−9n+26. Given two positive integers m and n, we describe how to construct two… (More)

- Vida Dujmovic, William S. Evans, Stephen G. Kobourov, Giuseppe Liotta, Christophe Weibel, Stephen K. Wismath
- Graph Drawing
- 2010

For a set S of n lines labeled from 1 to n, we say that S supports an n-vertex planar graph G if for every labeling from 1 to n of its vertices, G has a straight-line crossing-free drawing with each vertex drawn as a point on its associated line. It is known from previous work [4] that no set of n parallel lines supports all n-vertex planar graphs. We show… (More)