K. Aberer and M. Hauswirth, An overview of peer-to-peer information systems, WDAS, pp.171-188, 2002.

L. Addario-berry, B. Balle, and G. Perarnau, Diameter and stationary distribution of random r-out digraphs, 2015.

D. Angluin and D. Chen, Learning a Random DFA from Uniform Strings and State Information, The 26th International Conference on Algorithmic Learning Theory, p.2015, 2015.
DOI : 10.1007/978-3-319-24486-0_8

J. Ardnt, Generating Random Permutations, 2009.

S. Arora and B. Barak, Computational complexity : a modern approach, 2009.
DOI : 10.1017/CBO9780511804090

J. Aspnes and G. Shah, Skip graphs, ACM Transactions on Algorithms, vol.3, issue.4, p.37, 2007.
DOI : 10.1145/1290672.1290674

A. Barabasi, Linked : How everything is connected to everything else and what it means, 2002.

A. Barabási and R. Albert, Emergence of scaling in random networks, science, vol.286, issue.5439, pp.509-512, 1999.

F. Bassino, J. David, and C. Nicaud, Average Case Analysis of Moore???s State Minimization Algorithm, Algorithmica, vol.22, issue.9, pp.509-531, 2012.
DOI : 10.1007/s00453-011-9557-7

V. Batagelj and U. Brandes, Efficient generation of large random networks, Physical Review E, vol.71, issue.3, p.36113, 2005.
DOI : 10.1103/PhysRevE.71.036113

M. Bayati, J. H. Kim, and A. Saberi, A Sequential Algorithm for Generating Random Graphs, Algorithmica, vol.20, issue.3, pp.860-910, 2010.
DOI : 10.1007/s00453-009-9340-1

A. Edward and . Bender, The asymptotic number of non-negative integer matrices with given row and column sums, Discrete Mathematics, vol.10, issue.2, pp.217-223, 1974.

L. Blum, M. Shub, and S. Smale, On a theory of computation and complexity over the real numbers : np-completeness, recursive functions BIBLIOGRAPHIE and universal machines, Bulletin, vol.21, issue.1, pp.1-46, 1989.

T. Bohman and A. Frieze, Hamilton cycles in 3-out. Random Structures & Algorithms, pp.393-417, 2009.

B. Bollobás, A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs, European Journal of Combinatorics, vol.1, issue.4, pp.311-316, 1980.
DOI : 10.1016/S0195-6698(80)80030-8

B. Bollobás, Degree sequences of random graphs, Discrete Mathematics, vol.33, issue.1, pp.1-19, 1981.
DOI : 10.1016/0012-365X(81)90253-3

B. Bollobás, The evolution of random graphs. Transactions of the, pp.257-274, 1984.

B. Bollobás, W. Fernandez-de, and L. Vega, The diameter of random regular graphs, Combinatorica, vol.12, issue.2, pp.125-134, 1982.
DOI : 10.1007/BF02579310

B. Bollobás and O. Riordan, The Diameter of a Scale-Free Random Graph, Combinatorica, vol.24, issue.1, pp.5-34, 2004.
DOI : 10.1007/s00493-004-0002-2

B. Bollobás, Random Graphs, 2001.

V. Bourassa and F. Holt, Swan : Small-world wide area networks, Proceeding of International Conference on Advances in Infrastructures, 2003.

K. Briggs, L. Song, and T. Prellberg, A note on the distribution of the maximum of a set of poisson random variables, 2009.

K. Bringmann and T. Friedrich, Exact and Efficient Generation of Geometric Random Variates and Random Graphs, Automata, Languages, and Programming, pp.267-278, 2013.
DOI : 10.1007/978-3-642-39206-1_23

I. Clarke, O. Sandberg, B. Wiley, W. Theodore, and . Hong, Freenet: A Distributed Anonymous Information Storage and Retrieval System, Designing Privacy Enhancing Technologies, pp.46-66, 2001.
DOI : 10.1007/3-540-44702-4_4

B. Cohen, The bittorrent protocol specification, 2008.

C. Cooper, M. Dyer, and C. Greenhill, Sampling Regular Graphs and a Peer-to-Peer Network, Combinatorics, Probability and Computing, vol.16, issue.04, pp.557-593, 2007.
DOI : 10.1017/S0963548306007978

C. Cooper, R. Klasing, and T. Radzik, A randomized algorithm for the joining protocol in dynamic distributed networks, Theoretical Computer Science, vol.406, issue.3, pp.248-262, 2008.
DOI : 10.1016/j.tcs.2008.06.049
URL : https://hal.archives-ouvertes.fr/inria-00070627

J. David, Génération aléatoire d'automates et analyse d'algorithmes de minimisation, 2010.

P. Rémond-de-montmort, Essay d'analyse sur les jeux de hazard Réimprimé en, Chez Claude Jombert, et Jacque Quillau, 1714.

J. Désarménien, Une autre interprétation du nombre de dérangements, Actes 8e Sém, pp.11-16, 1984.

L. Devroye, Non-Uniform Random Variate Generation, 1986.
DOI : 10.1007/978-1-4613-8643-8

A. Duch, Randomized Insertion and Deletion in Point Quad Trees, Algorithms and Computation, pp.415-426, 2005.
DOI : 10.1007/978-3-540-30551-4_37

A. Duch, V. Estivill-castro, and C. Martinez, Randomized K-Dimensional Binary Search Trees, 1998.
DOI : 10.1007/3-540-49381-6_22

P. Duchon and R. Duvignau, Local Update Algorithms for Random Graphs, LATIN 2014 : Theoretical Informatics, pp.367-378, 2014.
DOI : 10.1007/978-3-642-54423-1_32
URL : https://hal.archives-ouvertes.fr/hal-01015599

P. Duchon and R. Duvignau, A new generation tree for permutations , preserving the number of fixed points, 26th International Conference on Formal Power Series and Algebraic Combinatorics DMTCS Proceedings, pp.679-690, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01015604

R. Durstenfeld, Algorithm 235: Random permutation, Communications of the ACM, vol.7, issue.7, p.420, 1964.
DOI : 10.1145/364520.364540

P. Erd?s, Graph theory and probability. ii. In Canad, J. Math. Citeseer, 1960.

P. Erdös, Some remarks on the theory of graphs, Bulletin of the American Mathematical Society, vol.53, issue.4, pp.292-294, 1947.
DOI : 10.1090/S0002-9904-1947-08785-1

P. Erd?s, Graph theory and probability. Canad, J. Math, vol.11, pp.34-38, 1959.

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

P. Erd?s and A. Rényi, On the evolution of random graphs, Publ. Math. Inst. Hungar. Acad. Sci, vol.5, pp.17-61, 1960.

P. Erd?s and A. Rényi, On the evolution of random graphs, Bull. Inst. Internat. Statist, vol.38, issue.4, pp.343-347, 1961.

N. Evans, B. Polot, and C. Grothoff, Efficient and Secure Decentralized Network Size Estimation, NETWORKING 2012, pp.304-317
DOI : 10.1007/978-3-642-30045-5_23

C. Fan, E. Mervin, I. Muller, and . Rezucha, Development of Sampling Plans by Using Sequential (Item by Item) Selection Techniques and Digital Computers, Journal of the American Statistical Association, vol.1, issue.298, pp.387-402, 1962.
DOI : 10.1080/01621459.1962.10480667

I. Trevor, A. M. Fenner, and . Frieze, On the connectivity of random morientable graphs and digraphs, Combinatorica, vol.2, issue.4, pp.347-359, 1982.

I. Trevor, A. M. Fenner, and . Frieze, On the existence of hamiltonian cycles in a class of random graphs. Discrete mathematics, pp.301-305, 1983.

R. A. Fisher and F. Yates, Statistical Tables for Biological, Agricultural and Medical Research, 1938.

P. Flajolet, J. Peter, P. Grabner, H. Kirschenhofer, and . Prodinger, On Ramanujan's Q-function, Journal of Computational and Applied Mathematics, vol.58, issue.1, pp.103-116, 1995.
DOI : 10.1016/0377-0427(93)E0258-N

P. Flajolet and N. Saheb, The complexity of generating an exponentially distributed variate, Journal of Algorithms, vol.7, issue.4, pp.463-488, 1986.
DOI : 10.1016/0196-6774(86)90014-3
URL : https://hal.archives-ouvertes.fr/inria-00076400

M. Fouz, Randomized rumor spreading in social networks and complete graphs, 2012.

J. Frankel and T. Pepper, The gnutella project

N. Edgar and . Gilbert, Random graphs. The Annals of Mathematical Statistics, pp.1141-1144, 1959.

C. Grothoff, I. Patrascu, and K. Bennett, Tiberiu Stef, and Tzvetan Horozov. The gnet whitepaper, 2002.

A. Grzegorczyk, On the definitions of computable real continuous functions, Fundamenta Mathematicae, vol.44, issue.1, pp.61-71, 1957.

A. Dominique and . Heger, A disquisition on the performance behavior of binary search tree data structures, European Journal for the Informatics Professional, vol.5, issue.5, pp.67-75, 2004.

M. Heyer, Randomness Preserving Deletions on Special Binary Search Trees, Electronic Notes in Theoretical Computer Science, vol.225, pp.99-113, 2009.
DOI : 10.1016/j.entcs.2008.12.069

N. Thomas and . Hibbard, Some combinatorial properties of certain trees with applications to searching and sorting, Journal of the ACM (JACM), vol.9, issue.1, pp.13-28, 1962.

W. Hörmann, The generation of binomial random variates, Journal of Statistical Computation and Simulation, vol.8, issue.1-2, pp.101-110, 1993.
DOI : 10.1145/355744.355749

D. Karger, E. Lehman, T. Leighton, R. Panigrahy, M. Levine et al., Consistent hashing and random trees, Proceedings of the twenty-ninth annual ACM symposium on Theory of computing , STOC '97, pp.654-663, 1997.
DOI : 10.1145/258533.258660

L. Katz, Probability of indecomposability of a random mapping function. The Annals of Mathematical Statistics, pp.512-517, 1955.

J. Han, K. Van, and H. Vu, Generating random regular graphs, Proceedings of the thirty-fifth annual ACM symposium on Theory of computing, pp.213-222, 2003.

D. Gary and . Knott, Deletion in Binary Storage Trees, p.7525557, 1975.

E. Donald and . Knuth, Deletions that preserve randomness, IEEE Transactions on Software Engineering, vol.5, pp.351-359, 1977.

E. Donald and . Knuth, The Art of Computer Programming) : Seminumerical Algorithms, 1997.

E. Donald and . Knuth, The Art of Computer Programming) Sorting and Searching, 1998.

E. Donald, . Knuth, C. Andrew, and . Yao, The complexity of nonuniform random number generation, Proceedings of Symposium on Algorithms and Complexity, pp.357-428, 1976.

A. Erwan-le-merrer, L. Kermarrec, and . Massoulie, Peer to peer size estimation in large and dynamic networks: A comparative study, 2006 15th IEEE International Conference on High Performance Distributed Computing, pp.7-17, 2006.
DOI : 10.1109/HPDC.2006.1652131

D. Liben-nowell, H. Balakrishnan, and D. Karger, Analysis of the evolution of peer-to-peer systems, Proceedings of the twenty-first annual symposium on Principles of distributed computing , PODC '02, pp.233-242, 2002.
DOI : 10.1145/571825.571863

G. Marsaglia, W. W. Tsang, and J. Wang, Fast Generation of Discrete Random Variables, Journal of Statistical Software, vol.11, issue.3, pp.1-11, 2004.
DOI : 10.18637/jss.v011.i03

C. Martínez, A. Panholzer, and H. Prodinger, Generating Random Derangements, Proc. of the 10th ACM-SIAM Workshop on Algorithm Engineering and Experiments (ALENEX) and the 5th ACM-SIAM Workshop on Analytic Algorithmics and Combinatorics (ANALCO), pp.234-240, 2008.
DOI : 10.1137/1.9781611972986.7

C. Martínez and S. Roura, Randomized binary search trees, Journal of the ACM, vol.45, issue.2, pp.288-323, 1998.
DOI : 10.1145/274787.274812

Y. Matias and Y. Afek, Simple and efficient election algorithms for anonymous networks, Distributed Algorithms, pp.183-194, 1989.
DOI : 10.1007/3-540-51687-5_42

R. Motwani and P. Raghavan, Randomized algorithms, Chapman & Hall/CRC, 2010.

G. Pandurangan, P. Raghavan, and E. Upfal, Building lowdiameter peer-to-peer networks. Selected Areas in Communications, IEEE Journal on, vol.21, issue.6, pp.995-1002, 2003.

D. Peleg, Distributed computing. SIAM Monographs on discrete mathematics and applications, 2000.

Y. Peres, Iterating von neumann's procedure for extracting random bits. The Annals of Statistics, pp.590-597, 1992.

K. Thomas, . Philips, F. Donald, . Towsley, K. Jack et al., On the diameter of a class of random graphs. Information Theory, IEEE Transactions on, vol.36, issue.2, pp.285-288, 1990.

J. Pouwelse and P. Garbacki, Dick Epema, and Henk Sips. The bittorrent p2p file-sharing system : Measurements and analysis. In Peer-to-Peer Systems IV, pp.205-216, 2005.

D. Price, Sizing the piracy universe. Netnames. http ://copyrightalliance .org/sites/default/files/ 2013-netnames-piracy.pdf, 2013.

W. Pugh, Skip lists: a probabilistic alternative to balanced trees, Communications of the ACM, vol.33, issue.6, pp.668-676, 1990.
DOI : 10.1145/78973.78977

D. Qiu and R. Srikant, Modeling and performance analysis of bittorrent-like peer-to-peer networks, In ACM SIGCOMM Computer Communication Review, vol.344, pp.367-378, 2004.

F. Rakotondrajao, k-fixed-points-permutations, INTEGERS : Electronic Journal of Combinatorial Number Theory, p.36, 2007.

R. Sedgewick and P. Flajolet, An introduction to the analysis of algorithms, 2013.

R. Seidel and C. R. Aragon, Randomized search trees, Algorithmica, vol.23, issue.4-5, pp.464-497, 1996.
DOI : 10.1007/BF01940876

J. Neil, . Sloane, and . Others, The OEIS Foundation Inc) The on-line encyclopedia of integer sequences, 2015.

A. Steger, C. Nicholas, and . Wormald, Generating Random Regular Graphs Quickly, Combinatorics, Probability and Computing, vol.8, issue.4, pp.377-396, 1999.
DOI : 10.1017/S0963548399003867

I. Stoica, R. Morris, D. Karger, F. Kaashoek, and H. Balakrishnan, Chord : A scalable peer-to-peer lookup service for internet applications

J. Von-neumann, Various techniques used in connection with random digits, NBS Appl. Math. Series, vol.36, p.12, 1951.

C. Wang and B. Li, Peer-to-peer overlay networks : A survey, p.9, 2003.

M. Wojciechowski, M. Capot?, J. Pouwelse, and A. Iosup, BTWorld, Proceedings of the 19th ACM International Symposium on High Performance Distributed Computing, HPDC '10, pp.581-588, 2010.
DOI : 10.1145/1851476.1851562

C. Nicholas and . Wormald, The asymptotic connectivity of labelled regular graphs, Journal of Combinatorial Theory, Series B, vol.31, issue.2, pp.156-167, 1981.

C. Nicholas and . Wormald, Generating random regular graphs, Journal of Algorithms, vol.5, issue.2, pp.247-280, 1984.

C. Nicholas and . Wormald, Models of random regular graphs, pp.239-298, 1999.

O. Ya?an and A. M. Makowski, Connectivity results for sensor networks under a random pairwise key predistribution scheme, Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on, pp.1797-1801, 2012.