f-vectors of Minkowski additions of convex polytopes
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Convex polyhedra are important objects in various areas of mathematics and other disciplines. A fundamental result, known as Minkowski-Weyl theorem, states that every polyhedron admits two types of representations, either as the solution set to a finite sy ...
EPFL2005
In this paper we consider the problem of computing sets of observable states for discrete-time, piecewise affine systems. When the maximal set of observable states is full-dimensional, we provide an algorithm for reconstructing it up to a zero measure set. ...
2005
We consider the problem of listing faces of the Minkowski sum of several V-polytopes in R^d. An algorithm for listing all faces of dimension up to j is presented, for any given 0
In polyhedral studies of 0/1 polytopes two prominent problems exist. One is the vertex enumeration problem: Given a system of inequalities, enumerate its feasible 0/1 points. Another one is the convex hull problem: Given a set of 0/1 points in dimension d, ...
We consider the following integer feasibility problem: Given positive integer numbers a0, a1,&mellip;,an with gcd(a1,&mellip;,an) = 1 and a = (a1,&mellip;,an), does there exist a ...
Polyhedral operations play a central role in constrained control. One of the most fundamental operations is that of projection, required both by addition and multiplication. This thesis investigates projection and its relation to multi-parametric linear op ...
In this paper we introduce a new algorithm called Equality Set Projection (ESP) for computing the orthogonal projection of bounded, convex polytopes. Our solution addresses the case where the input polytope is represented as the intersection of a finite nu ...
The notion of similarity between texts is fundamental for many applications of Natural Language Processing. For example, this notion is particularly useful for the applications designed for the management of information in large textual databases, such as ...
In this paper we address the problem of computing a minimal representation of the convex hull of the union of k H- polytopes in . Our method applies the reverse search algorithm to a shelling ordering of the facets of the convex hull. Efficient wrapping is ...
