Network flows: theory, algorithms, and applications, 1993. ,
Automatic translation of FORTRAN programs to vector form, ACM Transactions on Programming Languages and Systems, vol.9, issue.4, pp.491-542, 1987. ,
DOI : 10.1145/29873.29875
Implementing radixsort, Journal of Experimental Algorithmics, vol.3, 1998. ,
DOI : 10.1145/297096.297136
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.4536
A Polynomial Time Algorithm for Solving Systems of Linear Inequalities with Two Variables Per Inequality, SIAM Journal on Computing, vol.9, issue.4, pp.827-845, 1980. ,
DOI : 10.1137/0209063
The Parma Polyhedra Library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems, Science of Computer Programming, vol.72, issue.1-2, pp.3-21, 2008. ,
DOI : 10.1016/j.scico.2007.08.001
Weakly-relational shapes for numeric abstractions: improved algorithms and proofs of correctness. Formal Methods in System Design, pp.279-323, 2009. ,
A technique for summarizing data access and its use in parallelism enhancing transformations, PLDI, pp.41-53, 1989. ,
Loop Transformations for Restructuring Compilers: The Foundations, 1992. ,
DOI : 10.1007/b102311
On a routing problem, Quarterly of Applied Mathematics, vol.16, issue.1, pp.87-90, 1958. ,
DOI : 10.1090/qam/102435
The Polyhedral Model Is More Widely Applicable Than You Think, Proceedings of the International Conference on Compiler Construction (ETAPS CC'10), number 6011, 2010. ,
DOI : 10.1007/978-3-642-11970-5_16
URL : https://hal.archives-ouvertes.fr/inria-00551087
Solving Real-World Linear Programs: A Decade and More of Progress, Operations Research, vol.50, issue.1, pp.3-15, 2002. ,
DOI : 10.1287/opre.50.1.3.17780
A static analyzer for large safety-critical software, PLDI, pp.196-207, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00128135
A practical automatic polyhedral parallelizer and locality optimizer, PLDI, pp.101-113, 2008. ,
Circuit retiming applied to decomposed software pipelining, IEEE Transactions on Parallel and Distributed Systems, vol.9, issue.1, pp.24-35, 1998. ,
DOI : 10.1109/71.655240
URL : https://hal.archives-ouvertes.fr/hal-00856850
Shortest-path feasibility algorithms, Journal of Experimental Algorithmics, vol.14, pp.7-9, 2010. ,
DOI : 10.1145/1498698.1537602
Improved Algorithms For Linear Inequalities with Two Variables Per Inequality, SIAM Journal on Computing, vol.23, issue.6, pp.1313-1350, 1994. ,
DOI : 10.1137/S0097539791256325
Why does Astrée scale up? Formal Methods in System Design, pp.229-264, 2009. ,
Linear Programming and Extensions, 1963. ,
DOI : 10.1515/9781400884179
Loop Shifting for Loop Compaction, Int. J. Parallel Program, vol.28, issue.5, pp.499-534, 2000. ,
DOI : 10.1007/3-540-44905-1_26
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.1440
Complexity of Multi-dimensional Loop Alignment, Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science, STACS '02, pp.179-191, 2002. ,
DOI : 10.1007/3-540-45841-7_14
Scheduling and Automatic Parallelization, 2000. ,
DOI : 10.1007/978-1-4612-1362-8
URL : https://hal.archives-ouvertes.fr/hal-00856645
Optimal fine and medium grain parallelism detection in polyhedral reduced dependence graphs, Proceedings of the 1996 Conference on Parallel Architectures and Compilation Technique, pp.447-496, 1997. ,
DOI : 10.1109/PACT.1996.552676
URL : https://hal.archives-ouvertes.fr/hal-00856886
Testing the necklace condition for shortest tours and optimal factors in the plane, Theoretical Computer Science, vol.66, issue.2, pp.157-180, 1989. ,
DOI : 10.1016/0304-3975(89)90133-3
Parametric integer programming, RAIRO - Operations Research, vol.22, issue.3, pp.243-268, 1988. ,
DOI : 10.1051/ro/1988220302431
Some efficient solutions to the affine scheduling problem. I. One-dimensional time, International Journal of Parallel Programming, vol.40, issue.6, pp.313-348, 1992. ,
DOI : 10.1007/BF01407835
Some efficient solutions to the affine scheduling problem. Part II. Multidimensional time, International Journal of Parallel Programming, vol.2, issue.4, pp.389-420, 1992. ,
DOI : 10.1007/BF01379404
Scalable and Structured Scheduling, International Journal of Parallel Programming, vol.28, issue.6, pp.459-487, 2006. ,
DOI : 10.1007/s10766-006-0011-4
Forward Communication Only Placements and Their Use for Parallel Program Construction, Lecture Notes in Computer Science, vol.2481, pp.16-30, 2002. ,
DOI : 10.1007/11596110_2
Polly -Polyhedral Optimization in LLVM, IMPACT 2011, 2011. ,
Some ways to reduce the space dimension in polyhedra computations, Formal Methods in System Design, vol.29, issue.1, pp.79-95, 2006. ,
DOI : 10.1007/s10703-006-0013-2
URL : https://hal.archives-ouvertes.fr/hal-00189633
Simple and Fast Algorithms for Linear and Integer Programs with Two Variables Per Inequality, SIAM Journal on Computing, vol.23, issue.6, pp.1179-1192, 1994. ,
DOI : 10.1137/S0097539793251876
Beyond finite domains, Lecture Notes in Computer Science, vol.874, pp.86-94, 1994. ,
DOI : 10.1007/3-540-58601-6_92
Apron: A Library of Numerical Abstract Domains for Static Analysis, CAV, pp.661-667, 2009. ,
DOI : 10.1007/978-3-642-02658-4_52
URL : https://hal.archives-ouvertes.fr/hal-00786354
The Computational Complexity of Simultaneous Diophantine Approximation Problems, SIAM Journal on Computing, vol.14, issue.1, pp.196-209, 1985. ,
DOI : 10.1137/0214016
Communication-free parallelization via affine transformations, POPL, pp.201-214, 1997. ,
DOI : 10.1007/BFb0025873
Efficient and exact data dependence analysis, Proceedings of the ACM SIGPLAN 1991 conference on Programming language design and implementation, PLDI '91, pp.1-14, 1991. ,
The octagon abstract domain. Higher-Order and Symbolic Computation, pp.31-100, 2006. ,
Loop transformations: convexity, pruning and optimization, POPL, pp.549-562, 2011. ,
DOI : 10.1145/1925844.1926449
URL : https://hal.archives-ouvertes.fr/inria-00551077
The polybench benchmarks ,
Two easy theories whose combination is hard, Massachusetts Institute of Technology, 1977. ,
A practical algorithm for exact array dependence analysis, Communications of the ACM, vol.35, issue.8, pp.102-114, 1992. ,
DOI : 10.1145/135226.135233
A counterexample to the Hirsch Conjecture, Annals of Mathematics, vol.176, issue.1, pp.383-412, 2012. ,
DOI : 10.4007/annals.2012.176.1.7
Theory of linear and integer programming, 1986. ,
On solving boolean combinations of UTVPI constraints, Journal on Satisfiability Boolean Modeling and Computation (JSAT), vol.3, issue.12, pp.67-90, 2007. ,
Deciding Linear Inequalities by Computing Loop Residues, Journal of the ACM, vol.28, issue.4, pp.769-779, 1981. ,
DOI : 10.1145/322276.322288
URL : http://www.dtic.mil/get-tr-doc/pdf?AD=ADA055868
The two variable per inequality abstract domain, Higher-Order and Symbolic Computation, vol.1, issue.1, pp.87-143, 2010. ,
DOI : 10.1007/s10990-010-9062-8
Smoothed analysis of algorithms, Journal of the ACM, vol.51, issue.3, pp.385-463, 2004. ,
DOI : 10.1145/990308.990310
A decision method for elementary algebra and geometry. Univ. of California Press, 1951. ,
The many facets of linear programming, Mathematical Programming, vol.91, issue.3, pp.417-436, 2002. ,
DOI : 10.1007/s101070100261
Graphite two years after: First lessons learned from real-world polyhedral compilation, GCC Research Opportunities Workshop (GROW'10), 2010. ,
URL : https://hal.archives-ouvertes.fr/inria-00551516
Scalability Challenges in the Polyhedral Model: An Algorithmic Approach using (Unit-)Two-variable Per Inequality Sub- Polyhedra, 2013. ,
Potential and Challenges of Two- Variable-Per-Inequality Sub-Polyhedral Compilation, First International Workshop on Polyhedral Compilation Techniques (IM- PACT'11), in conjunction with CGO'11, 2011. ,
A Case for Strongly Polynomial Time Sub-Polyhedral Scheduling Using Two-Variable-Per-Inequality Polyhedra, Second International Workshop on Polyhedral Compilation Techniques (IMPACT'12), in conjunction with HiPEAC'12, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00786832
Scalable Program Optimization Techniques In The Polyhedral Model, 2007. ,
On the optimality of feautrier's scheduling algorithm. Concurrency and Computation: Practice and Experience, pp.1047-1068, 2003. ,
Minimal enclosing parallelepiped in 3D, Computational Geometry, vol.29, issue.3, pp.177-190, 2004. ,
DOI : 10.1016/j.comgeo.2004.01.009
URL : https://hal.archives-ouvertes.fr/inria-00071901
A polynomial combinatorial algorithm for generalized minimum cost flow, Proceedings of the thirty-first annual ACM symposium on Theory of computing, STOC '99, pp.11-18, 1999. ,
A loop transformation theory and an algorithm to maximize parallelism, IEEE Transactions on Parallel and Distributed Systems, vol.2, issue.4, pp.452-471, 1991. ,
DOI : 10.1109/71.97902
Minimal data dependence abstractions for loop transformations, Lecture Notes in Computer Science, vol.892, pp.201-216, 1994. ,
DOI : 10.1007/BFb0025880
Lectures on polytopes. Graduate texts in mathematics, 2006. ,