Proofs of the Parisi and Coppersmith-Sorkin conjectures for the finite random assignment problem

Annual Symposium on Foundations of Computer Science - Proceedings

Volumn , Issue , 2003, Pages 168-178

  Nair, Chandra ^a   Prabhakar, Balaji ^a   Sharma, Mayank ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; CONFORMAL MAPPING; JOB ANALYSIS; MATRIX ALGEBRA; OPTIMIZATION; PROBABILITY DISTRIBUTIONS;

COPPERSMITH-SORKIN CONJECTURES; FINITE RANDOM ASSIGNMENT PROBLEM; PARISI CONJECTURES; PROBABILISTIC ARGUMENTS;

THEOREM PROVING;

EID: 0344550525     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (26)

1. D. J. Aldous. Asymptotics in the random assignment problem. Probab. Th. Rel. Fields, 93:507-534, 1992.
2. D. J. Aldous. The ζ (2) limit in the random assignment problem. Random Structures and Algorithms, 18:381-418, 2001.
3. S. E. Alm and G. Sorkin. Exact expectations and distributions for the random assignment problem. Combinatorics, Probability, and Computing, 11(3):217-248, 2002.
4. Brunetti, Krauth, Mézard, and Parisi. unpublished.
5. M. W. Buck, C. C. S. and D. P. Robbins. On the expected value of the minimum assignment. Random Structures and Algorithms, 21:33-58, 2002.
6. D. Coppersmith and G. Sorkin. Constructive bounds and exact expectations for the random assignment problem. Random Structures and Algorithms, 15:113-144, 1999.
7. D. Coppersmith and G. Sorkin. On the expected incremental cost of a minimum assignment. Chapter 8: Contemporary Combinatorics, Bolyai Society Mathematical Studies, Springer, 10, 2002.
8. V. S. Dotsenko. Exact solution of the random bipartite matching model. J. Phys. A, 33:2015-2030, 2000.
9. M. X. Goemans and M. S. Kodialam. A lower bound on the expected cost of an optimal assignment. Math. Oper. Res., 18:267-274, 1993.
10. R. M. Karp. An upper bound on the expected cost of an optimal assignment. Technical Report, Computer Science Division, U.C. Berkeley, 1984.
11. R. M. Karp. An upper bound on the expected cost of an optimal assignment. Discrete Algorithms and Complexity: Proceedings of the Japan-U.S. Joint Seminar, pages 1-4, 1987.
12. R. M. Karp, A. H. G. Rinnooy Kan, and R. Vohra. Average case analysis of a heuristic for the assignment problem. Mathematics of Operations Research, 19(3):513-522, 1994.
13. A. Lazarus. Certain expected values in the random assignment problem. Oper. Res. Letters, 14:207-214, 1993.
14. S. Linusson and J. Wastlund. A generalization of the random assignment problem. http://www.mai.liu.se/svlin, 2000.
15. S. Linusson and J. Wastlund. A proof of Parisi's conjecture on the random assignment problem. http://www.mai.liu.se/jowas, 2003.
16. M. Mézard and G. Parisi. On the solution of the random link matching problem. J. Physique, 48:1451-1459, 1987.
17. M. Mézard, G. Parisi, and M. A. Virasoro. Spin Glass Theory and Beyond. World Scientific, Singapore, 1987.
18. C. Nair. Towards the resolution of Coppersmith-Sorkin conjectures. Proceedings of the 40th Annual Allerton Conference on Communication, Control and Computing, 2002.
19. C. Nair, B. Prabhakar, and M. Sharma. Proofs of the Parisi and Coppersmith-Sorkin conjectures for the finite random assignment problem. http://www.stanford.edu/mchandra, 2003.
20. B. Olin. Asymptotic Properties of Random Assignment Problems. Ph.D. Thesis, Kungl Tekniska Hogskolan, Stockholm, Sweden, 1992.
21. G. Parisi. A conjecture on random bipartite matching. Technical Report cond-mat/9801176, XXX LANL Archive, 1998.
22. M. Sharma and B. Prabhakar. On Parisi's conjecture for the finite random assignment problem. Proceedings of the 40th Annual Allerton Conference on Communication, Control and Computing, 2002.
23. M. Sharma and B. Prabhakar. On Parisi's conjecture for the finite random assignment problem. http://www.stanford.edu/msharma, 2003.
24. J. M. Steele. Probability Theory and Combinatorial Optimization. SIAM, Philadelphia, PA, 1997.
25. M. Talagrand. An assignment problem at high temperature. To appear in Annals of Probability, 2002.
26. D. W. Walkup. On the expected value of a random assignment problem. SIAM J. Comput., 8:440-442, 1979.