. .. Cost-matrices,

, 3.2 Existing Generation Methods of Contingency Tables . . 100 6.3.3 Uniform MCMC Generation of Cost Matrices, p.101

P. Statement and . .. Contribution, 103 the generated constrained cost matrices and we prove that our experiments are consistent with previous studies in the literature, Journal of Parallel and Distributed Computing, vol.73, issue.10, pp.1362-1374, 2013.

S. Aap-+-16]-mishra-ashish, V. Aditya, . Pranet, R. Abhijit-r-asati, and . Solomon, A modular approach to random task graph generation, Indian Journal of Science and Technology, vol.9, issue.8, 2016.

H. Arabnejad and J. G. Barbosa, List scheduling algorithm for heterogeneous systems by an optimistic cost table, IEEE Transactions on Parallel and Distributed Systems, vol.25, issue.3, pp.682-694, 2014.

K. M. Thomas-l-adam, J. R. Chandy, and . Dickson, A comparison of list schedules for parallel processing systems, Communications of the ACM, vol.17, issue.12, pp.685-690, 1974.

A. V. Aho, R. Michael, J. D. Garey, and . Ullman, The transitive reduction of a directed graph, SIAM Journal on Computing, vol.1, issue.2, pp.131-137, 1972.

K. Robert and . Armstrong, Investigation of effect of different run-time distributions on smartnet performance, 1997.

I. Ahmad and Y. Kwok, On exploiting task duplication in parallel program scheduling, IEEE Transactions on Parallel & Distributed Systems, vol.9, pp.872-892, 1998.

M. Aggarwal, D. Robert, A. Kent, and . Ngom, Genetic algorithm based scheduler for computational grids, High Performance Computing Systems and Applications, 2005. HPCS 2005. 19th International Symposium on, pp.209-215, 2005.

G. Di-george-amalarethinam and . Mary, DAGEN-A Tool To Generate Arbitrary Directed Acyclic Graphs Used For Multiprocessor Scheduling, International Journal of Research and Reviews in Computer Science, vol.2, issue.3, p.782, 2011.

. Asm-+-00]-shoukat, H. J. Ali, M. Siegel, D. Maheswaran, S. Hensgen et al., Representing task and machine heterogeneities for heterogeneous computing systems, Tamkang J. Sci. Engineer, vol.3, issue.3, pp.195-208, 2000.

S. Ali, H. J. Siegel, M. Maheswaran, and D. Hensgen, Task execution time modeling for heterogeneous computing systems, Heterogeneous Computing Workshop (HCW), pp.185-199, 2000.

A. F. Virgílio, . Almeida, J. Vasconcelos, . Nagib-cotrimárabe, and . Menascé, Using random task graphs to investigate the potential benefits of heterogeneity in parallel systems, Proceedings of the 1992 ACM/IEEE conference on Supercomputing, pp.683-691, 1992.

J. Benesty, J. Chen, Y. Huang, and I. Cohen, Pearson correlation coefficient, Noise reduction in speech processing, pp.1-4, 2009.

B. Bodin, Y. Lesparre, J. Delosme, and A. Munier-kordon, Fast and efficient dataflow graph generation, Proceedings of the 17th International Workshop on Software and Compilers for Embedded Systems, pp.40-49, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01084899

, Béla Bollobás. Random Graphs, 2001.

N. Cdb-+-16]-pedro-campos, C. Dahir, M. Bonney, A. Trefzer, G. Tyrrell et al., Xl-stage: A cross-layer scalable tool for graph generation, evaluation and implementation, Embedded Computer Systems: Architectures, Modeling and Simulation (SAMOS), 2016 International Conference on, pp.354-359, 2016.

M. Cdg-+-06]-mary-cryan, L. A. Dyer, M. Goldberg, R. Jerrum, and . Martin, Rapidly mixing markov chains for sampling contingency tables with a constant number of rows, SIAM Journal on Comp, vol.36, pp.247-278, 2006.

Y. Chen, P. Diaconis, P. Susan, J. Holmes, and . Liu, Sequential monte carlo methods for statistical analysis of tables, Journal of the American Statistical Association, vol.100, issue.469, pp.109-120, 2005.

M. E. Louis-claude-canon, P. Sayah, and . Héam, A Markov Chain Monte Carlo Approach to Cost Matrix Generation for Scheduling Performance Evaluation, International Conference on High Performance Computing & Simulation (HPCS), 2018.

L. Canon, P. Héam, and L. Philippe, Controlling the correlation of cost matrices to assess scheduling algorithm performance on heterogeneous platforms. Concurrency and Computation: Practice and Experience, vol.29, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02392532

C. E. Thomas-h-cormen, R. L. Leiserson, C. Rivest, and . Stein, Introduction to algorithms, 2009.

D. Cordeiro, G. Mounié, S. Perarnau, D. Trystram, J. Vincent et al., Random graph generation for scheduling simulations, Proceedings of the 3rd international ICST conference on simulation tools and techniques, vol.60, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00471255

M. Cosnard and M. Marrakchi, Yves Robert, and Denis Trystram. Parallel gaussian elimination on an mimd computer, Parallel Computing, vol.6, issue.3, pp.275-296, 1988.

L. Louis-claude-canon, B. Marchal, F. Simon, and . Vivien, Online scheduling of task graphs on hybrid platforms, European Conference on Parallel Processing, pp.192-204, 2018.

L. , C. Canon, and L. Philippe, On the heterogeneity bias of cost matrices for assessing scheduling algorithms, IEEE Transactions on Parallel and Distributed Systems, vol.28, issue.6, pp.1675-1688, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01664636

M. E. Louis-claude-canon, P. Sayah, and . Héam, A comparison of random task graph generation methods for scheduling problems, 2019.

D. Dbgl-+-97]-giuseppe, A. Battista, G. Garg, R. Liotta, E. Tamassia et al., An experimental comparison of four graph drawing algorithms, Computational Geometry, vol.7, issue.5-6, pp.303-325, 1997.

P. Diaconis and L. Coste, Random walk on contingency tables with mixed row and column sums, 1995.

P. Duchon, P. Flajolet, G. Louchard, and G. Schaeffer, Boltzmann samplers for the random generation of combinatorial structures, Combinatorics, Probability & Computing, vol.13, issue.4-5, pp.577-625, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00307530

M. Dyer and C. Greenhill, Polynomial-time counting and sampling of two-rowed contingency tables, Theoretical Computer Science, vol.246, issue.1-2, pp.265-278, 2000.

M. E. Dyer and C. S. Greenhill, Polynomial-time counting and sampling of two-rowed contingency tables, Theor. Comput. Sci, vol.246, issue.1-2, pp.265-278, 2000.

P. Dutot, F. Tchimou-n'takpé, H. Suter, and . Casanova, Scheduling parallel task graphs on (almost) homogeneous multicluster platforms, IEEE Transactions on Parallel and Distributed Systems, vol.20, issue.7, pp.940-952, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00347273

P. Robert, D. L. Dick, W. Rhodes, and . Wolf, Bernd Sturmfels, et al. Algebraic algorithms for sampling from conditional distributions, Proceedings of the 6th international workshop on Hardware/software codesign, vol.26, pp.363-397, 1998.

T. Davidovi?, D. Milica?elmi?, D. Teodorovi?, and . Ramljak, Bee colony optimization for scheduling independent tasks to identical processors, Journal of heuristics, vol.18, issue.4, pp.549-569, 2012.

A. Denise and P. Zimmermann, Uniform random generation of decomposable structures using floating-point arithmetic, Theor. Comput. Sci, vol.218, issue.2, pp.233-248, 1999.
URL : https://hal.archives-ouvertes.fr/inria-00073447

D. Eaton and K. Murphy, Bayesian structure learning using dynamic programming and mcmc, 2012.

P. Erd?s and A. Rényi, On random graphs I, Publ. Math. Debrecen, vol.6, pp.290-297, 1959.

R. Fagin, Probabilities on finite models, J. Symb. Log, vol.41, issue.1, pp.50-58, 1976.

F. Fga-+-98-;-richard, M. Freund, S. Gherrity, M. Ambrosius, M. Campbell et al., Scheduling resources in multi-user, heterogeneous, computing environments with SmartNet, Heterogeneous Computing Workshop (HCW), pp.184-199, 1998.

. George-s-fishman, Counting contingency tables via multistage markov chain monte carlo, Journal of Computational and Graphical Statistics, vol.21, issue.3, pp.713-738, 2012.

F. Lester-randolph and D. R. Fulkerson, Flows in networks, 2016.

P. Flajolet and R. Sedgewick, Analytic combinatorics, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00072739

I. Gupta, A. Choudhary, and P. Jana, Generation and proliferation of random directed acyclic graphs for workflow scheduling problem, Proceedings of the 7th International Conference on Computer and Communication Technology, pp.123-127, 2017.

M. R. Garey and D. S. Johnson, Strong NP-completeness results: motivation, examples, and implications, J. Assoc. Comput. Mach, vol.25, issue.3, pp.499-508, 1978.

R. L. Graham, E. L. Lawler, J. K. Lenstra, and A. H. Rinnooy-kan, Optimization and approximation in deterministic sequencing and scheduling: a survey, Annals of Discrete Mathematics, vol.5, pp.287-326, 1979.

J. Geweke and S. Porter-hudak, The estimation and application of long memory time series models, Journal of time series analysis, vol.4, issue.4, pp.221-238, 1983.

A. Gelman and . Donald-b-rubin, Inference from iterative simulation using multiple sequences, Statistical science, vol.7, issue.4, pp.457-472, 1992.

A. Gupta and J. Rawlings, Comparison of parameter estimation methods in stochastic chemical kinetic models: examples in systems biology, AIChE Journal, vol.60, issue.4, pp.1253-1268, 2014.

R. L. Graham, Bounds on Multiprocessing Timing Anomalies, Journal of Applied Mathematics, vol.17, issue.2, pp.416-429, 1969.

T. Hagras and J. Janecek, A simple scheduling heuristic for heterogeneous computing environments, International Symposium on Parallel and Distributed Computing, p.104, 2003.

J. Shinsuke-ide and F. Gagliardi-cozman, Random generation of bayesian networks, Advances in Artificial Intelligence, 16th Brazilian Symposium on Artificial Intelligence, SBIA 2002, pp.366-375, 2002.

H. Oscar, C. E. Ibarra, and . Kim, Heuristic Algorithms for Scheduling Independent Tasks on Nonidentical Processors, Journal of the ACM, vol.24, issue.2, pp.280-289, 1977.

H. Oscar, C. Ibarra, and . Kim, Heuristic algorithms for scheduling independent tasks on nonidentical processors, Journal of the ACM (JACM), vol.24, issue.2, pp.280-289, 1977.

E. Ilavarasan and P. Thambidurai, Low complexity performance effective task scheduling algorithm for heterogeneous computing environments, Journal of Computer sciences, vol.3, issue.2, pp.94-103, 2007.

A. Jcd-+-13]-gideon-juve, E. Chervenak, S. Deelman, G. Bharathi, K. Mehta et al., Characterizing and profiling scientific workflows, Future Generation Computer Systems, vol.29, issue.3, pp.682-692, 2013.

Y. Kwok and I. Ahmad, Benchmarking and comparison of the task graph scheduling algorithms, Journal of Parallel and Distributed Computing, vol.59, issue.3, pp.381-422, 1999.

Y. Kwok and I. Ahmad, Link contention-constrained scheduling and mapping of tasks and messages to a network of heterogeneous processors, Cluster Computing, vol.3, issue.2, pp.113-124, 2000.

J. Kuipers and G. Moffa, Uniform random generation of large acyclic digraphs, Statistics and Computing, vol.25, issue.2, pp.227-242, 2015.

B. Karrer, E. J. Mark, and . Newman, Random graph models for directed acyclic networks, Physical Review E, vol.80, issue.4, p.46110, 2009.

. Valentin-fedorovich-kolchin, Boris Aleksandrovich Sevastyanov, and Vladimir Pavlovich Chistyakov. Random allocations, 1978.

R. Kolisch, A. Sprecher, and A. Drexl, Characterization and generation of a general class of resource-constrained project scheduling problems, Management science, vol.41, issue.10, pp.1693-1703, 1995.

J. Li, K. Agrawal, C. Lu, and C. Gill, Outstanding paper award: Analysis of global edf for parallel tasks, Real-Time Systems (ECRTS), 2013 25th Euromicro Conference on, pp.3-13, 2013.

Y. T. Joseph and . Leung, Handbook of scheduling: algorithms, models, and performance analysis, 2004.

V. Liskovets, On the number of maximal vertices of a random acyclic digraph, Theory Probab. Appl, vol.20, issue.2, pp.401-409, 1975.

R. E. Lord, S. Janusz, . Kowalik, P. Swarn, and . Kumar, Solving linear algebraic equations on an mimd computer, Journal of the ACM (JACM), vol.30, issue.1, pp.103-117, 1983.

D. A. Levin, Y. Peres, and E. L. Wilmer, Markov chains and mixing times, 2006.

W. Mantel, Problem 28, Wiskundige Opgaven, vol.10, p.320, 1907.

A. Martinez, Synthetic loads analysis of directed acyclic graphs for scheduling tasks, International Journal of Advanced Computer Science and Applications, vol.9, issue.3, pp.347-354, 2018.

I. Guy-melançon, M. Dutour, and . Bousquet-mélou, Random generation of directed acyclic graphs, Electronic Notes in Discrete Mathematics, vol.10, pp.202-207, 2001.

N. Mki-+-03]-ron-milo, S. Kashtan, . Itzkovitz, E. J. Mark, U. Newman et al., On the uniform generation of random graphs with prescribed degree sequences, 2003.

G. Melançon and F. Philippe, Generating connected acyclic digraphs uniformly at random, Inf. Process. Lett, vol.90, issue.4, pp.209-213, 2004.

J. Nichols and T. Warnow, Tutorial on computational linguistic phylogeny, Language and Linguistics Compass, vol.2, issue.5, pp.760-820, 2008.

S. +-18]-julian-oppermann, M. Vollbrecht, O. Reuter-oppermann, A. Sinnen, and . Koch, GeMS: a generator for modulo scheduling problems: work in progress, Proceedings of the International Conference on Compilers, Architecture and Synthesis for Embedded Systems, p.7, 2018.

K. Pearson, On the theory of contengency and its relation to association and normal correlation. Drapers' Company Reserach Memoirs, 1904.

D. Anatoly and . Plotnikov, Experimental algorithm for the maximum independent set problem, 2007.

R. W. Robinson, Counting labeled acyclic digraphs, New Directions in the Theory of Graphs, pp.239-273, 1973.

A. Rishad, . Shafik, M. Bashir, J. S. Al-hashimi, and . Reeve, Systemlevel design optimization of reliable and low power multiprocessor system-on-chip, Microelectronics Reliability, vol.52, pp.1735-1748, 2012.

S. Stuijk, M. Geilen, and T. Basten, SDF 3 : SDF for Free, Application of Concurrency to System Design, pp.276-278, 2006.

B. Saovapakhiran, G. Michailidis, and M. Devetsikiotis, Aggregated-dag scheduling for job flow maximization in heterogeneous cloud computing, Global Telecommunications Conference (GLOBECOM 2011), pp.1-6, 2011.

D. Sullivan, What is google pagerank? a guide for searchers & webmasters. SearchEngineLand, vol.26, pp.70426-011828, 2007.

R. Sakellariou and H. Zhao, A hybrid heuristic for dag scheduling on heterogeneous systems, Parallel and Distributed Processing Symposium, p.111, 2004.

H. Topcuoglu, S. Hariri, and M. Wu, Performanceeffective and low-complexity task scheduling for heterogeneous computing, IEEE transactions on parallel and distributed systems, vol.13, pp.260-274, 2002.

H. Topcuoglu, S. Hariri, and M. Wu, Performanceeffective and low-complexity task scheduling for heterogeneous computing, IEEE Trans. on Parallel and Dist. Systems, vol.13, issue.3, pp.260-274, 2002.

T. Tobita and H. Kasahara, A standard task graph set for fair evaluation of multiprocessor scheduling algorithms, Journal of Scheduling, vol.5, issue.5, pp.379-394, 2002.

J. D. Ullman, NP-complete scheduling problems, J. Comput. System Sci, vol.10, pp.384-393, 1975.

M. Wu and D. D. Gajski, Hypertool: A programming aid for message-passing systems, IEEE transactions on parallel and distributed systems, vol.1, issue.3, pp.330-343, 1990.

P. Winkler, Random orders, Order, vol.1, issue.4, pp.317-331, 1985.

T. Yang and A. Gerasoulis, DSC: Scheduling parallel tasks on an unbounded number of processors, IEEE Transactions on Parallel and Distributed Systems, vol.5, issue.9, pp.951-967, 1994.