J. M. Anderson and M. S. Lam, Global optimizations for parallelism and locality on scalable parallel machines, ACM Sigplan Notices, vol.28, issue.6, pp.112-125, 1993.
DOI : 10.1145/155090.155101

J. W. Cassels, Rational Quadratic Forms, 1978.
DOI : 10.1016/s0304-0208(08)70410-9

T. Chen and J. Sheu, Communication-free data allocation techniques for parallelizing compilers on multicomputers, IEEE Transactions on Parallel and Distributed Systems, vol.5, issue.9, pp.924-938, 1994.
DOI : 10.1109/icpp.1993.56

A. Darte and Y. Robert, Mapping uniform loop nests onto distributed memory architectures, Parallel Computing, vol.20, pp.679-710, 1994.
DOI : 10.1016/0167-8191(94)90001-9
URL : https://hal.archives-ouvertes.fr/hal-00857077

A. Darte and Y. Robert, On the alignment problem, Parallel Processing Letters, vol.4, issue.3, pp.259-270, 1994.
URL : https://hal.archives-ouvertes.fr/hal-00857081

D. Mich-ele and Y. Robert, Mapping aane loop nests: New results, High-Performance Computing and Networking, International Conference and Exhibition, v olume LCNS 919, pp.184-189, 1995.

J. R. Evans and E. Minieka, Optimization Algorithms for Networks and Graphs, 1992.

P. Feautrier, Some eecient solutions to the ane scheduling problem, part II, multidimensional time, Int. J. Parallel Programming, vol.21, issue.6, pp.389-420, 1992.
DOI : 10.1007/bf01379404

P. Feautrier, Towards automatic distribution, Parallel Processing Letters, vol.4, issue.3, pp.233-244, 1994.

H. Michael and G. , Automatic parallelization for distributed-memory multiprocessing systems, 1989.

E. Hecke, Lectures on the Theory of Algebraic Numbers, 1981.

C. H. Huang and P. Sadayappan, Communication-free hyperplane partitioning of nested loops, Languages and Compilers for Parallel Computing, pp.186-200, 1991.
DOI : 10.1007/bfb0038665

K. Knobe, J. D. Lukas, and G. L. Steele, Data optimization: Allocation of arrays to reduce communication on SIMD machines, Journal of Parallel and Distributed Computing, vol.8, pp.102-118, 1990.

A. Korganoo and M. Pavel-parvu, El ements de th eorie des matrices carr ees et rectangles en analyse num erique. Dunod, 1966.

J. Li and M. Chen, The data alignment phase in compiling programs for distributed memory machines, Journal of Parallel and Distributed Computing, vol.13, pp.213-221, 1991.

J. D. Lukas, Data locality for shared memory. I n Sixth SIAM Conf. Parallel Processing for Scientiic Computing, pp.836-839, 1993.

J. D. Lukas and K. Knobe, Data optimization and its eeect on communication costs in MIMD fortran code, Fifth SIAM Conf. Parallel Processing for Scientiic Computing, pp.478-483, 1992.

M. Newman, Integral Matrices, 1972.

A. Platonoo, Contribution a la Distribution Automatique des Donn ees pour Machines Massivement Parall eles, 1995.

W. Shang and Z. Shu, Data alignment of loop nests without nonlocal communications, Application Speciic Array Processors, pp.439-450, 1994.

C. Tseng, An Optimizing Fortran D Compiler for MIMD Distributed-Memory Machines, 1993.

M. Wolfe, The Tiny loop restructuring research tool, International Conference on Parallel Processing, vol.II, pp.46-53, 1991.