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Abstract: . In the area of automatic parallelization of programs, analyzing and transforming loop nests with parametric affine loop bounds requires fundamental mathematical results. The most common geometrical model of iteration spaces, called the polytope model, is based on mathematics dealing with convex and discrete geometry, linear programming, combinatorics and geometry of numbers. In this paper, we present automatic methods for computing the parametric vertices and the Ehrhart polynomial, i.e. a... (Update)
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BibTeX entry: (Update)
Clauss, Ph. and Loechner V. Parametric Analysis of Polyhedral Iteration Spaces. In International Conference ASAP'96, Chicago, Illinois, August 1996, pp 415--424. http://citeseer.ist.psu.edu/article/clauss98parametric.html More
@inproceedings{ philippe96parametric,
author = "Clauss, Philippe and Loechner, Vincent",
title = "{P}arametric {A}nalysis of {P}olyhedral {I}teration {S}paces",
booktitle = "{IEEE} Int. Conf. on Application Specific Array Processors, {ASAP}'96",
month = "August",
publisher = "IEEE Computer Society",
year = "1996",
url = "citeseer.ist.psu.edu/article/clauss98parametric.html" }
Citations (may not include all citations):717 Theory of Linear and Integer Programming (context) - Schrijver - 1986
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67 Dataflow analysis of scalar and array references (context) - Feautrier - 1991
62 Geometry of Numbers (context) - Gruber, Lekkerkerker - 1987
60 A practical data flow framework for array reference analysis.. - Duesterwald, Gupta et al. - 1993
36 Theory and Algorithms (context) - Bazaraa, Sherali et al. - 1993
28 A survey and comparison of methods for finding all vertices .. (context) - Mattheiss, Rubin - 1980
26 Sur un probl`eme de g'eom'etrie diophantienne lin'eaire II (context) - Ehrhart - 1967
26 Sur un probl`eme de g'eom'etrie diophantienne lin'eaire (context) - Ehrhart - 1967
26 Polynomes arithm'etiques et M'ethode des Poly`edres en Combi.. (context) - Ehrhart - 1977
24 Calculus of space-optimal mappings of systolic algorithms on.. (context) - Clauss, Mongenet et al. - 1992
24 Enumerative Combinatorics Volume (context) - Stanley - 1986
22 Estimation of nested loop execution time by integer arithmet.. (context) - Tawbi - 1994
22 Footprints in the cache (context) - Stone, Thiebaut - 1986
16 Processor allocation and loop scheduling on multiprocessor c.. (context) - Tawbi, Feautrier - 1992
16 Symbolic analysis: A basis for parallelization (context) - Haghighat, Polychronopoulos - 1993
12 Polynomials associated with finite cell-complexes (context) - Macdonald - 1971
11 edres rationnels homoth (context) - Ehrhart, poly - 1962
9 The volume of a lattice polyhedron (context) - Macdonald - 1963
7 The volume of a lattice polyhedron to enumerate processors a.. - Clauss - 1995
6 Advances in Languages and Compilers for Parallel Processing (context) - Ferrante, Sarkar et al. - 1991
5 Also published as IRISA technical report PI (context) - Wilde, for et al. - 1993
5 ACM SIGPLAN Conference on Programming Language Design and Im.. (context) - Pugh, to et al. - 1994
4 of the 6th annual worshop on Programming Languages and Compi.. (context) - Haghighat, Polychronopoulos et al. - 1993
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The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://icps.u-strasbg.fr/Ehrhart/Ehrhart.html):
The Volume of a Lattice Polyhedron to Enumerate Processors and.. - Clauss (1996) (Correct)
Handling Memory Cache Policy with Integer Points Countings - Clauss (1997) (Correct)
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