,. S. Laksono-adhianto, M. W. Banerjee, M. Fagan, G. Krentel, J. M. Marin et al., HPCTOOLKIT: tools for performance analysis of optimized parallel programs, Concurrency and Computation: Practice and Experience, vol.22, pp.685-701, 2010.

A. Aggarwal and J. S. Vitter, The Input/Output Complexity of Sorting and Related Problems, Commun. ACM, vol.31, pp.1116-1127, 1988.
URL : https://hal.archives-ouvertes.fr/inria-00075827

G. Ballard, E. Carson, J. Demmel, M. Hoemmen, N. Knight et al., Communication lower bounds and optimal algorithms for numerical linear algebra, Acta Numerica, vol.23, pp.1-155, 2014.

G. Ballard, J. Demmel, O. Holtz, and O. Schwartz, Minimizing Communication in Numerical Linear Algebra, SIAM J. Matrix Analysis Applications, vol.32, pp.866-901, 2011.

G. Ballard, J. Demmel, O. Holtz, and O. Schwartz, Graph expansion and communication costs of fast matrix multiplication, J. ACM, vol.59, p.32, 2012.

A. I. Barvinok, A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed, Mathematics of Operations Research, vol.19, pp.769-779, 1994.

C. Bauer, A. Frink, and R. Kreckel, Introduction to the GiNaC Framework for Symbolic Computation within the C++ Programming Language, J. Symbolic Computation, vol.33, pp.1-12, 2002.

G. Bilardi and E. Peserico, A characterization of temporal locality and its portability across memory hierarchies, Automata, Languages and Programming, pp.128-139, 2001.

G. Bilardi, M. Scquizzato, and F. Silvestri, A Lower Bound Technique for Communication on BSP with Application to the FFT, Euro-Par 2012 Parallel Processing -18th International Conference, pp.676-687, 2012.

M. Christ, J. Demmel, N. Knight, T. Scanlon, and K. Yelick, Communication Lower Bounds and Optimal Algorithms for Programs That Reference Arrays -Part 1, 2013.

J. Demmel, L. Grigori, M. Hoemmen, and J. Langou, Communication-optimal Parallel and Sequential QR and LU Factorizations, SIAM J. Scientific Computing, vol.34, pp.206-239, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00870930

V. Elango, F. Rastello, L. Pouchet, J. Ramanujam, and P. Sadayappan, On characterizing the data movement complexity of computational DAGs for parallel execution, Proc. of the 26th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA '14, pp.296-306, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01016090

V. Elango, F. Rastello, L. Pouchet, J. Ramanujam, and P. Sadayappan, On Characterizing the Data Access Complexity of Programs, Proc. of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp.567-580, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01104556

P. Feautrier, Parametric integer programming, RAIRO Recherche Opérationnelle, vol.22, pp.243-268, 1988.

P. Feautrier, Some efficient solutions to the affine scheduling problem. I. One-dimensional time, International Journal of Parallel Programming, vol.21, pp.313-347, 1992.

P. Feautrier and C. Lengauer, Polyhedron model, Encyclopedia of Parallel Computing, pp.1581-1592, 2011.

M. Frigo, C. E. Leiserson, H. Prokop, and S. Ramachandran, Cache-Oblivious Algorithms, Proc. of the 40th Annual Symposium on Foundations of Computer Science, FOCS '99, pp.17-18, 1999.

J. Hong and H. T. Kung, I/O complexity: The red-blue pebble game, Proc. of the 13th Annual ACM Symposium on Theory of Computing (STOC '81), pp.326-333, 1981.

D. Irony, S. Toledo, and A. Tiskin, Communication lower bounds for distributed-memory matrix multiplication, J. Parallel and Distrib. Comput, vol.64, pp.1017-1026, 2004.

G. Kwasniewski, M. Kabic, M. Besta, J. Vandevondele, R. Solcà et al., Red-blue pebbling revisited: near optimal parallel matrix-matrix multiplication, Proc. of the International Conference for High Performance Computing, Networking, Storage and Analysis, vol.24, p.22, 2019.

H. Lynn, H. Loomis, and . Whitney, An inequality related to the isoperimetric inequality, Bull. Am. Math. Soc, vol.55, pp.961-962, 1949.

A. Olivry, J. Langou, L. Pouchet, P. Sadayappan, and F. Rastello, Automated Derivation of Parametric Data Movement Lower Bounds for Affine Programs, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02421026

L. Pouchet and T. Yuki, , 2015.

J. Ramanujam and P. Sadayappan, Tiling multidimensional iteration spaces for multicomputers, J. Parallel and Distrib. Comput, vol.16, pp.108-230, 1992.

D. Ranjan, J. E. Savage, and M. Zubair, Upper and Lower I/O Bounds for Pebbling r-Pyramids, Combinatorial Algorithms -21st International Workshop, IWOCA 2010, 2010.

D. Ranjan, J. E. Savage, and M. Zubair, Strong I/O Lower Bounds for Binomial and FFT Computation Graphs, Computing and Combinatorics, vol.6842, pp.134-145, 2011.

D. Ranjan, J. E. Savage, and M. Zubair, Upper and lower I/O bounds for pebbling r-pyramids, J. Discrete Algorithms, vol.14, pp.2-12, 2012.

J. E. Savage, Extending the Hong-Kung model to memory hierarchies, Computing and Combinatorics, vol.959, pp.270-281, 1995.

J. E. Savage and M. Zubair, A unified model for multicore architectures, Proc. of the 1st international forum on Next-generation multicore/manycore technologies, 2008.

T. Smith, B. Lowery, J. Langou, and R. A. Van-de-geijn, A Tight I/O Lower Bound for Matrix Multiplication, 2019.

. Volker-strassen, Gaussian elimination is not optimal, Numerische mathematik, vol.13, pp.354-356, 1969.

S. Verdoolaege, ISL: An integer set library for the polyhedral model, Mathematical Software-ICMS 2010, pp.299-302, 2010.

S. Verdoolaege, Integer Set Library: Manual, 2018.

S. Verdoolaege and T. Grosser, Polyhedral Extraction Tool, Second International Workshop on Polyhedral Compilation Techniques (IMPACT'12), 2012.

S. Williams, A. Waterman, and D. Patterson, Roofline: an insightful visual performance model for multicore architectures, Commun. ACM, vol.52, pp.65-76, 2009.