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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 an automatic method for computing the number of integer points contained in a convex polytope... (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/clauss96parametric.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/clauss96parametric.html" }
Citations (may not include all citations):717 Theory of Linear and Integer Programming (context) - Schrijver - 1986
86 Combinatorics and Commutative Algebra (context) - Stanley - 1983
72 Counting Solutions to Linear and Nonlinear Constraints throu.. - Clauss - 1996
62 Geometry of Numbers (context) - Gruber, Lekkerkerker - 1987
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 Polynomes arithm'etiques et M'ethode des Poly`edres en Combi.. (context) - Ehrhart - 1977
26 Sur un probl`eme de g'eom'etrie diophantienne lin'eaire (context) - Ehrhart - 1967
24 Enumerative Combinatorics Volume (context) - Stanley - 1986
22 Estimation of nested loop execution time by integer arithmet.. (context) - Tawbi - 1994
16 Symbolic analysis: A basis for parallelization (context) - Haghighat, Polychronopoulos - 1993
16 Processor allocation and loop scheduling on multiprocessor c.. (context) - Tawbi, Feautrier - 1992
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 Research Report ICPS (context) - Loechner, Wilde et al. - 1995
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
1 Polynomials associated with Parametric Analysis of Polyhedra.. (context) - Macdonald - 1971
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