Delayed path coupling and generating random permutations

Random Structures and Algorithms

Volumn 17, Issue 3-4, 2000, Pages 238-259

  Czumaj, Artur ^a   Kutyłowski, Mirostaw ^b  

^a NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

^b ADAM MICKIEWICZ UNIVERSITY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039032193     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/1098-2418(200010/12)17:3/4<238::AID-RSA4>3.0.CO;2-E     Document Type: Article

References (39)

1. D. Aldous, "Random walks of finite groups and rapidly mixing Markov chains," in Séminaire de Probabilités XVII, 1981/82, Volume 986 of Lecture Notes in Mathematics, J. Azéma and M. Yor (Editors), Springer-Verlag, Berlin, 1983, pp. 243-297.
2. D. Aldous and P. Diaconis, Shuffling cards and stopping times, Am Math Month 93 (1986), 333-347.
3. R. Anderson. "Parallel algorithms for generating random permutations on a shared memory machine," in Proceedings of the 2nd Annual ACM Symposium on Parallel Algorithms and Architectures, Island of Crete, Greece, 2-6 July 1990. ACM Press, New York, NY, 1990, pp. 95-102.
4. R.J. Anderson and G.L. Miller, Optical communication for pointer based algorithms, Tech. Rep. CRI 88-14, University of Southern California, 1988.
5. R. Bubley and M. Dyer, "Path coupling: A technique for proving rapid mixing in Markov chains," in Proceedings of the 38th Symposium on Foundations of Computer Science, Miami Beach, FL, 19-22 October 1997. IEEE Computer Society Press, Los Alamitos, CA, pp. 223-231.
6. R. Bubley and M. Dyer, "Faster random generation of linear extensions," in Proceedings of the 9th ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, 25-27 January 1998. SIAM, Philadelphia, PA, pp. 355-363.
7. R. Bubley, M. Dyer, and C. Greenhill, "Beating the 2△ bound for approximately counting colourings: A computer-assisted proof of rapid mixing," in Proceedings of the 9th ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, 25-27 January 1998. SIAM, Philadelphia, PA, pp. 355-363.
8. A. Czumaj, "Recovery time of dynamic allocation processes," in Proceedings of the 10th Annual ACM Symposium on Parallel Algorithms and Architectures, Puerto Vallarta, Mexico, 28 June-2 July 1998. ACM Press, New York, NY, pp. 202-211.
9. A. Czumaj, P. Kanarek, M. Kutyłowski, and K. Loryś, Fast generation of random permutations via network simulation, Algorithmica, 21(1) (1998) 2-20. A preliminary version appeared in Proceedings of the 4th Annual European Symposium on Algorithms, Volume 1136 of Lecture Notes in Computer Science, Barcelona, Spain, 25-27 September 1996, J. Diaz and M. Serna (Editors), Springer-Verlag, Berlin, pp. 246-260.
10. A. Czumaj, P. Kanarek, M. Kutyłowski, and K. Loryś, Fast generation of random permutations via network simulation, Algorithmica, 21(1) (1998) 2-20. A preliminary version appeared in Proceedings of the 4th Annual European Symposium on Algorithms, Volume 1136 of Lecture Notes in Computer Science, Barcelona, Spain, 25-27 September 1996, J. Diaz and M. Serna (Editors), Springer-Verlag, Berlin, pp. 246-260.
11. A. Czumaj, P. Kanarek, M. Kutyłowski, and K. Loryś, "Delayed path coupling and generating random permutations via distributed stochastic processes," in Proceedings of the 10th ACM-SIAM Symposium on Discrete Algorithms, Baltimore, MD, 17-19 January 1999. SIAM, Philadelphia, PA, pp. 271-280.
12. P. Diaconis, Group Representations in Probability and Statistics, Volume 11 of Lecture Notes-Monograph Series. Institute of Mathematical Statistics, Hayward, CA, 1988.
13. P. Diaconis, M. Mc Grath, and J. Pitman, Riffle shuffles, cycles, and descents, Combinatorica, 15(1) (1995), 11-29.
14. P. Diaconis and M. Shahshahani, Generating a random permutation with random transpositions, Zeitschrift Wahrscheinlichkeitstheorie verwandte Gebiete, 57 (1981), 159-179.
15. M. Dyer, A. Frieze, and R. Kannan, A random polynomial-time algorithm for approximating the volume of convex bodies, J ACM 38(1) (1991), 1-17. A preliminary version appeared in Proceedings of the 21st ACM Symposium on Theory of Computing, Seattle, Washington, 15-17 May 1989, ACM Press, New York, NY, pp. 297-307.
16. M. Dyer, A. Frieze, and R. Kannan, A random polynomial-time algorithm for approximating the volume of convex bodies, J ACM 38(1) (1991), 1-17. A preliminary version appeared in Proceedings of the 21st ACM Symposium on Theory of Computing, Seattle, Washington, 15-17 May 1989, ACM Press, New York, NY, pp. 297-307.
17. M. Dyer and C. Greenhill, "A genuinely polynomial-time algorithm for sampling two-rowed contingency tables," in Proceedings of the 25th Annual International Colloquium on Automata, Languages and Programming, Volume 1443 of Lecture Notes in Computer Science, K.G. Larsen, S. Skyum, and G. Winskel (Editors), Aalborg, Denmark, 13-17 July 1998. Springer-Verlag, Berlin, pp. 339-350.
18. M. Dyer and C. Greenhill, A more rapidly mixing Markov chain for graph colourings, Ran Struct Algorith 13(3-4) (1998), 285-317.
19. M. Dyer and C. Greenhill, "Random walks on combinatorial objects," in Surveys in Combinatorics, Volume 267 of London Mathematical Society Lecture Note Series, J.D. Lamb and D.A. Preece (Editors), Cambridge University Press, 1999, pp. 101-136.
20. P.B. Gibbons, Y. Matias, and V. Ramachandran, Efficient low-contention parallel algorithms, J Comput Syst Sci 53(3) (1996), 417-442. A preliminary version appeared in Proceedings of the 6th ACM Symposium on Parallel Algorithms and Architectures, Padua, Italy, 24-26 June 1996, ACM Press, New York, NY, pp. 236-247.
21. P.B. Gibbons, Y. Matias, and V. Ramachandran, Efficient low-contention parallel algorithms, J Comput Syst Sci 53(3) (1996), 417-442. A preliminary version appeared in Proceedings of the 6th ACM Symposium on Parallel Algorithms and Architectures, Padua, Italy, 24-26 June 1996, ACM Press, New York, NY, pp. 236-247.
22. P. Gibbons, Y. Matias, V. Ramachandran, The QRQW PRAM: Accounting for contention in parallel algorithms, SIAM J Comput 28(2) (1999), 733-769. A preliminary version appeared in Proceedings of the 5th ACM Symposium on Discrete Algorithms, Philadelphia, PA, 23-25 January 1994, SIAM, Philadelphia, PA, pp. 638-648.
23. P. Gibbons, Y. Matias, V. Ramachandran, The QRQW PRAM: Accounting for contention in parallel algorithms, SIAM J Comput 28(2) (1999), 733-769. A preliminary version appeared in Proceedings of the 5th ACM Symposium on Discrete Algorithms, Philadelphia, PA, 23-25 January 1994, SIAM, Philadelphia, PA, pp. 638-648.
24. L.A. Goldberg, M. Jerrum, T. Leighton, and S. Rao, Doubly logarithmic communication algorithms for optical-communication parallel computers, SIAM J Comput 26(4) (1997), 1100-1119. A preliminary version appeared in Proceedings of the 5th ACM Symposium on Parallel Algorithms and Architectures, Velen, Germany, 30 June-2 July 1993, ACM Press, New York, NY, pp. 300-309.
25. L.A. Goldberg, M. Jerrum, T. Leighton, and S. Rao, Doubly logarithmic communication algorithms for optical-communication parallel computers, SIAM J Comput 26(4) (1997), 1100-1119. A preliminary version appeared in Proceedings of the 5th ACM Symposium on Parallel Algorithms and Architectures, Velen, Germany, 30 June-2 July 1993, ACM Press, New York, NY, pp. 300-309.
26. T. Hagerup, "Fast parallel generation of random permutations," in Proceedings of the 18th Annual International Colloquium on Automata, Languages and Programming, Volume 510 of Lecture Notes in Computer Science, J.L. Albert, B. Monien, and M. Rodriguez-Artalejo (Editors), Madrid, Spain, 8-12 July 1991, Springer-Verlag Berlin, pp. 405-416.
27. M. Jerrum and A. Sinclair, "The Markov chain Monte Carlo method: An approach to approximate counting and integration," in Approximation Algorithms for script Nscript P sign-Hard Problems, Chapter 12, D.S. Hochbaum (Editor), PWS Publishing Company Boston, MA, 1996, pp. 482-520.
28. R. Kannan, "Markov chains and polynomial time algorithms," in Proceedings of the 35th Symposium on Foundations of Computer Science, Santa Fe, NM, 20-22 November 1994, IEEE Computer Society Press, Los Alamitos, CA, pp. 656-671.
29. T. Lindvall, Lectures on the Coupling Method, John Wiley & Sons, New York NY, 1992.
30. Y. Matias and U. Vishkin, "Converting high probability into nearly-constant time - with applications to parallel hashing," in Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, New Orleans, LA, 6-8 May 1991, ACM Press, New York NY, pp. 307-316.
31. G.L. Miller and J.H. Reif, "Parallel tree contraction," in Proceedings of the 26th Symposium on Foundations of Computer Science, Portland, OR, 21-23 October 1985, IEEE Computer Society Press, Los Alamitos, CA, pp. 478-489.
32. G.L. Miller and J.H. Reif, Parallel tree contraction, Part 1: Fundamentals Adv Comput Res 5 (1989), 47-72.
33. R. Motwani and P. Raghavan, Randomized algorithms. Cambridge University Press, Cambridge, 1995.
34. C. Rackoff and D.R. Simon, "Cryptographic defense against traffic analysis," in Proceedings of the 25th Annual ACM Symposium on Theory of Computing, San Diego, CA, 16-18 May 1993, ACM Press, New York, NY, pp. 672-681.
35. S. Rajasekaran and J.H. Reif, Optimal and sublogarithmic time randomized parallel sorting algorithms, SIAM J Comput 19 (1989), 594-607.
36. J.H. Reif, "An optimal parallel algorithm for integer sorting," in Proceedings of the 26th Symposium on Foundations of Computer Science, Portland, OR, 21-23 October 1985, IEEE Computer Society Press, Los Alamitos, CA, pp. 496-504.
37. A. Sinclair, Algorithms for Random Generation and Counting: A Markov Chain Approach, Birkhäuser, Boston, MA, 1993.
38. E. Vigoda, "Improved bounds for sampling colorings," in Proceedings of the 40th Symposium on Foundations of Computer Science, New York City, NY, 17-19 October 1999, IEEE Computer Society Press, Los Alamitos, CA.
39. M. Zito, I. Pu, M. Amos, and A. Gibbons, "ℛscript Nscript C sign algorithms for the uniform generation of combinatorial structures," in Proceedings of the 7th ACM-SIAM Symposium on Discrete Algorithms, Atlanta, GA, 28-30 January 1996, SIAM, Philadelphia, PA, pp. 429-437.