Generating random graphs with large girth

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2009, Pages 566-575

  Bayati, Mohsen ^a   Montanari, Andrea ^b   Saberi, Amin ^c  

^a MICROSOFT RESEARCH   (United Kingdom)

^b Stanford University   (United States)

^c STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FORWARD ERROR CORRECTION; GRAPHIC METHODS; POLYNOMIAL APPROXIMATION;

EMPTY GRAPH; LOW-DENSITY PARITY-CHECK (LDPC) CODES; POLYNOMIAL ALGORITHM; POLYNOMIAL-TIME; RANDOM GRAPHS; SEQUENTIAL PROCESS; SIMPLE AND EFFICIENT ALGORITHMS;

GRAPH THEORY;

EID: 70349113473     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611973068.63     Document Type: Conference Paper

References (42)

1. D. Alderson, J. Doyle, and W. Willinger, "Toward and Optimization-Driven Framework for Designing and Generating Realistic Internet Topologies", HotNets, 2002.
2. N. Alon and J. Spencer, "The Probabilistic Method", Wiley, NY, 1992.
3. A. Amraoui, A. Montanari and R. Urbanke, "How to Find Good Finite-Length Codes: From Art Towards Science", Eur. Trans. Telecomm. 18 (2007), 491-508 (Pubitemid 47218021)
4. M. Bayati, A. Montanari and A. Saberi, Generating Random Graphs with Large Girth, (2008) arXiv.
5. M. Bayati, J. H. Kim and A. Saberi, "A Sequential Algorithm for Generating Random Graphs", International Workshop on Randomization and Computation, 2007.
6. J. Blanchet, "Efficient Importance Sampling for Binary Contingency Tables", preprint, 2007.
7. J. Blitzstein and P. Diaconis, "A sequential importance sampling algorithm for generating random graphs with prescribed degrees", preprint, 2006.
8. B. Bollobás, and O. Riordan, "Constrained graph processes", Electronic Journal of Combinatorics, 7, 2000.
9. B. Bollobás, Random Graphs, Cambrdige University Press, 2001.
10. T. Bu and D. Towsley, "On Distinguishing between Internet Power Law Topology Generator", INFOCOM, 2002.
11. Y. Chen, P. Diaconis, S. Holmes and J.S. Liu, "Sequential Monte Carlo methods for statistical analysis of tables", Journal of the American Statistical Association 100, 109-120, 2005. (Pubitemid 40366822)
12. S. Y. Chung, G. D. Forney, Jr., T. Richardson and R. Urbanke, "On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit," IEEE Comm. Lett. 5 (2001), 58-60 (Pubitemid 32286625)
13. M. Faloutsos, P. Faloutsos and C. Faloutsos, "On Power-law Relationships of the Internet Topology", SIGCOM, 1999.
14. X. Hu, E. Eleftheriou and D. Arnold, "Progressive Edge-Growth Tanner Graphs", Proc. of GLOBECOM 01, San Antonio, USA, Nov 2001
15. X. Hu, E. Eleftheriou and D. Arnold, "Regular and irregular progressive edge-growth Tanner graphs", IEEE Trans. on Inform. Theory, 51 (2005), 386-398 (Pubitemid 40151893)
16. P. Erdocombining double acute accents, S. Suen, and P. Winkler, "On the size of a random maximal graph", Random Structure and Algorithms, 6, pp 309-318, 1995.
17. S. Janson, T. Luczak, and A. Rucinski, " Random Graphs", Wiley-Interscisnce, 2000.
18. J. H. Kim, V. H. Vu, "Generating random regular graphs", ACM Symposium on Theory of Computing (STOC), 213-222, 2003.
19. D. Knuth, "Mathematics and computer science: coping with finiteness", Science 194(4271):1235-1242, 1976.
20. R. Koetter and P. Vontobel, "Graph covers and iterative decoding of finite-lenght codes," Int. Conf. on Turbo codes and Rel. Topics, Brest, France, September 2003.
21. M. Luby, M. Mitzenmacher, A. Shokrollahi, D. A. Spielman and V. Stemann, "Practical Loss-Resilient Codes," 29th annual ACM Symposium on Theory of Computing (STOC), 1997, pp. 150-159
22. D. J. MacKay and M. S. Postol, "Weaknesses of Margulis and Ramanujan-Margulis Low-Density Parity-Check Codes", Elec. Notes in Theor. Comp. Science 74 (2003)
23. A. Medina, I. Matta and J. Byers, "On the origin of power laws in Internet topologies", ACM Computer Communication Review, vol.30, no.2, pp. 18-28, 2000.
24. R. Milo, S. ShenOrr, S. Itzkovitz, N. Kashtan, D. Chklovskii and U. Alon, "Network motifs: Simple building blocks of complex networks", Science 298, 824-827, 2002. (Pubitemid 35231534)
25. A. Montanari, "The asymptotic error floor of LDPC ensembles under BP decoding," 44rd Allerton Conference on Comm. Control and Comp., Monticello, IL, Sep 2006
26. J. M. F. Moura and J. Lu and H. Zhang "Structured low-density parity-check codes", IEEE Sign. Proc. Mag., 21 (2004), 42-55
27. D. Osthus, and A. Taraz, "Random maximal H-free graphs", Random Structures and Algorithms, 1999.
28. C. Di, D. Proietti, I. E. Teletar, T. J. Richardson and R. Urbanke, "Finite-length analysis of low-density parity-check codes on the binary erasure channel", IEEE Trans. Inform. Theory, 46 (2002) 1570-1579 (Pubitemid 34759861)
29. A. Ramamoorthy and R. Wesel, "Construction of short block length irregular low-density parity-check codes" IEEE Intern. Conf. on Comm., Paris, June 2004
30. T. Richardson, "Error floors of LDPC codes", 41st Allerton Conference on Comm. Control and Comp., Monticello, IL, Sep 2003
31. T. Richardson and R. Urbanke, Modern Coding Theory, Cambridge University Press, Cambridge 2008
32. J. Rosenthal and P. O. Vontobel, "Constructions of regular and irregular LDPC codes using Ramanujan graphs and ideas from Margulis", IEEE Symp. on Inform. Theory, Washington, June 2001
33. A. Rucinski, and N. Wormald, "Random graph processes with degree restrictions", Combin. Prob. Comput 1, pp 169-180, 1992.
34. A. Sinclair, "Algorithms for random generation and counting : a Markov chain approach", Birkhäuser, 1993.
35. A. Steger and N.C. Wormald, "Generating random regular graphs quickly", Combinatorics, Probab. and Comput (8), pp 377-396, 1999. (Pubitemid 129640093)
36. A. Steger, "On the Evolution of Triangle-Free Graphs", Combinatorics, Probability and Computing, 14, pp 211-224, 2005.
37. J. Spencer, "Counting extensions", J. Combin. Theory Ser. A 53, pp247-255, 1990.
38. J. Spencer, "Maximal triangle-free graphs and Ramsey R(3,t)", unpublished manuscript, 1995.
39. M. G. Stepanov, V. Y. Chernyak and M. Chertkov, "Diagnosis of weaknesses in modern error correction codes: a physics approach", Phys Rev. Lett. 95 (2005) 228701-228704
40. H. Tangmunarunkit, R.Govindan, S.Jamin, S.Shenker, and W.Willinger, "Network Topology Generators: Degree based vs. Structural", ACM SIGCOM, 2002.
41. N. C. Wormald, "Models of random regular graphs", Surveys in combinatorics (Canterbury) London Math. Soc. Lecture Notes Ser., Vol 265. Cambridge Univ. Press, Cambridge, 239-298, 1999.
42. H. Xiao and A. H. Banihashemi, "Improved progressive-edge-growth (PEG) construction of LDPC codes", Proc. of GLOBECOM 04, Dallas, USA, Nov 2004