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- G Corti˜nas, C Haesemeyer, M Schlichting, C Weibel
- 2005

We prove a blow-up formula for cyclic homology which we use to show that infinitesimal K-theory satisfies cdh-descent. Combining that result with some computations of the cdh-cohomology of the sheaf of regular functions, we verify a conjecture of Weibel predicting the vanishing of algebraic K-theory of a scheme in degrees less than minus the dimension of… (More)

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)

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)

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)

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)

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)