Automatic parallelization of nested loops, based on a mathematical model, the polytope model, has been improved significantly over the last decade: state-of-theart methods allow flexible distributions of computations in space and time, which lead to high-quality parallelism. However, these methods

In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also include a new inductive bound for the minimum distance of generalized toric codes. As an application, we give new formulas for the minimum

We consider cyclic d-polytopes P that are realizable with vertices on the moment curve Md: t − → (t, t2,..., td) of order d ≥ 3. A hyperplane H bisects a j-face of P if H meets its relative interior. For ` ≥ 1, we investigate the maximum number of vertices that P can have so that for some

Polytopic multiplexing is a new method of overlapping holograms that, when combined with other multiplexing techniques, can increase the capacity of a volume holographic data storage system by more than a factor of 10. This is because the method makes possible the effective utilization of thick

. The aim of this paper is to explain the importance of polytope and polyhedra in automatic parallelization. We show that the semantics of parallel programs is best described geometrically, as properties of sets of integral points in n-dimensional spaces, where n is related to the maximum nesting

A code polytope is defined to be the convex hull in R n of the points in {0, 1} n corresponding to the codewords of a binary linear code. This paper contains a collection of results concerning the structure of such code polytopes. A survey of known results on the dimension and the minimal

In the literature , we can nd now several ecient schedul ing and al location techniques which describe a performant parallel execution of l oop nests. Nevertheless, few works have been devoted to code generation expressing the parallel ism derived by those techniques. In [4 ], we proposed

In this paper, we explore a connection between binary hierarchical models, their marginal polytopes and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes

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