A proof of Parisi's conjecture on the random assignment problem

Probability Theory and Related Fields

Volumn 128, Issue 3, 2004, Pages 419-440

  Linusson, Svante ^a   Wästlund, Johan ^a  

^a LINKÖPING UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 12144287806     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-003-0308-9     Document Type: Article

References (24)

1. [A92] Aldous, D.: Asymptotics in the random assignment problem. Pr. Th. Related Fields 93, 507-534 (1992)
2. [A01] Aldous, D.: The ζ (2) limit in the random assignment problem. Random Structures Algorithms 18 (4), 381-418 (2001)
3. [AS02] Alm, S.E., Sorkin, G.B.: Exact expectations and distributions in the random assignment problem. Combin. Probab. Comput. 11 (3), 217-248 (2002)
4. [BFM98] Beveridge, A., Frieze, A.M., McDarmid Colin J.H.: Random minimum length spanning trees in regular graphs. Combinatorica 18, 311-333 (1998)
5. [BCR02] Buck, M.W., Chan, C.S., Robbins, D.P.: On the expected value of the minimum assignment. Random Structures Algorithms. 21 (1), 33-58 (2002)
6. [CS98] Coppersmith, D., Sorkin, G.B.: Constructive Bounds and Exact Expectations For the Random Assignment Problem. Random Structures Algorithms 15, 133-144 (1999)
7. [CS02] Coppersmith, D., Sorkin, G.B.: On the expected incremental cost of a minimum assignment. In: Contemporary Mathematics, B. Bollobás, (ed.), Vol. 10 of Bolyai Society Mathematical Studies, Springer
8. [EES01] Eriksson, H., Eriksson, K., Sjöstrand, J.: Exact expectation for random graphs and assignments. Proceedings of FPSAC 2001, Arizona
9. [FM89] Frieze, A.M., McDarmid Colin, J.H.: On random minimum spanning trees, Combinatorica 9, 1989
10. [F85] Frieze, A.M.: On the value of a random minimum spanning tree problem. Disc Appl. Math. 10, 47-56 (1985)
11. [GK93] Goemans, M.X., Kodialam, M.S.: A lower bound on the expected cost of an optimal assignment. Math. Oper. Res. 18, 267-274 (1993)
12. [K87] Karp, R.M.: An upper bound on the expected cost of an optimal assignment. In Discrete Algorithms and Complexity: Proceedings of the Japan-U.S. Joint Seminar, Academic Press, 1987, pp. 1-4
13. [L93] Lazarus, A.: Certain expected values in the random assignment problem. Oper. Res. Lett. 14, 207-214 (1993)
14. [LW00] Linusson, S., Wästlund, J.: A generalization of the random assignment problem. Unpublished manuscript. arXiv:math.CO/0006146
15. [LP86] Lovász, L., Plummer, M.D.: Matching Theory, North-Holland 1986
16. [MP85] Mézard, M., Parisi, G.: Replicas and optimization. J. Phys. Lett. 46, 771-778 (1985)
17. [MP87] Mézard, M., Parisi, G.: On the solution of the random link matching problems. J. Phys. Lett. 48, 1451-1459 (1987)
18. 1[N02] Nair, C.: Towards the resolution of Coppersmith-Sorkin conjectures. Proceedings of the 40th annual Allerton conference on communication, control and computing, 2002
19. [NPS03a] Nair, C., Prabhakar, B., Sharma, M.: A proof of the conjecture due to Parisi for the finite random assignment problem, available at http://www.stanford.edu/~balaji/rap.html
20. [NPS03b] Chandra Nair, Balaji Prabhakar, Mayank Sharma, Proofs of the Parisi and Coppersmith-Sorkin Conjectures for the Fininte Random Assignment Problem, Proceedings of IEEE FOCS, 2003
21. [O92] Olin, Birgitta, Asymptotic properties of the random assignment problem, Ph.D. thesis, Kungl Tekniska Högskolan, Stockholm, Sweden, 1992
22. [PR93] Pardalos, P.M., Ramakrishnan, K.G.: On the expected optimal value of random assignment problems: Experimental results and open questions. Comput. Optim. Appl. 2, 261-271 (1993)
23. [P98] Parisi, G.: A conjecture on random bipartite matching. Physics e-Print archive, http://xxx.lanl.gov/ps/cond-mat/9801176, January 1998
24. [W79] Walkup, D.W.: On the expected value of a random assignment problem. SIAM J. Comput. 8, 440-442 (1979)