Belief propagation: An asymptotically optimal algorithm for the random assignment problem

Mathematics of Operations Research

Volumn 34, Issue 2, 2009, Pages 468-480

  Salez, Justin ^a   Shah, Devavrat ^b  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Belief propagation; Correlation decay; Local weak convergence; Poisson weighted infinite tree; Random assignment problem

Indexed keywords

BELIEF PROPAGATION; CORRELATION DECAY; LOCAL WEAK CONVERGENCE; POISSON WEIGHTED INFINITE TREE; RANDOM ASSIGNMENT PROBLEM;

ASYMPTOTIC ANALYSIS; AUTOMATA THEORY; CONVERGENCE OF NUMERICAL METHODS; GRAPH THEORY; INTELLIGENT SYSTEMS; POISSON DISTRIBUTION; POISSON EQUATION; TRAVELING SALESMAN PROBLEM;

BACKPROPAGATION;

EID: 67649975560     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1090.0380     Document Type: Article

References (21)

1. Aldous, D. 1992. Asymptotics in the random assignment problem. Probab. Theory Related Fields 93 507-534.
2. Aldous, D. 2001. The ζ (2) limit in the random assignment problem. Random Structures Algorithms 18 381-418.
3. Aldous, D., A. Bandyopadhyay. 2005. A survey of max-type recursive distributional equations. Ann. Appl. Probab. 15(2) 1047-1110.
4. Aldous, D., J. M. Steele. 2003. The objective method: Probabilistic combinatorial optimization and local weak convergence. H. Kesten, ed. Probability and Discrete Structures, Vol. 110, Encyclopedia of Mathematical Sciences. Springer, 1-72.
5. Bandyopadhyay, A. 2002. Bivariate uniqueness in the logistic recursive distributional equation. Technical Report 629, Department of Statistics, University of California, Berkeley.
6. Bayati, M., D. Shah, M. Sharma. 2008. Max-product for maximum weight matching: Convergence, correctness, and LP duality. IEEE Trans. Inform. Theory 54(3) 1241-1251.
7. Billingsley, P. 1999. Convergence of Probability Measures. Wiley Series in Probability and Statistics, John Wiley & Sons, New York.
8. Coppersmith, D., G. Sorkin. 1999. Constructive bounds and exact expectations for the random assignment problem. Random Structures Algorithms 15 113-144.
9. Dyer, M. E., A. M. Frieze, C. J. H. McDiarmid. 1986. On linear programs with random costs. Math. Programming 35 3-16.
10. Edmonds, J., R. Karp. 1972. Theoretical improvements in algorithmic efficiency for network flow problems. J. ACM 19 248-264.
11. Goemans, M. X., M. S. Kodialam. 1993. A lower bound on the expected cost of an optimal assignment. Math. Oper. Res. 18 267-274.
12. Karp, R. M. 1980. An algorithm to solve the m × n assignment problem in expected time O(mnlogn), Networks 10 143-152.
13. Karp, R. M. 1987. An upper bound on the expected cost of an optimal assignment. D. Johnson, ed. Discrete Algorithms and Complexity: Proc. Japan-U.S. Joint Seminar. Academic Press, New York, 1-4.
14. Lazarus, A. 1993. Certain expected values in the random assignment problem. Oper. Res. Lett. 14 207-214.
15. Linusson, S., J. Wästlund. 2004. A proof of Parisi's conjecture on the random assignment problem. Probab. Theory Related Fields 128 419-440.
16. Mézard, M., G. Parisi. 1987. On the solution of the random link matching problem. J. Phys. 48 1451-1459.
17. Nair, C., B. Prabhakar, M. Sharma. 2005. Proofs of the Parisi and Coppersmith-Sorkin random assignment conjectures. Random Structures Algorithms 27(4) 413-444.
18. Olin, B. 1992. Asymptotic properties of random assignment problems. Ph.D. thesis, Kungl. Tekniska Högskolan, Stockholm.
19. Pearl, J. 1988. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco.
20. Walkup, D. W. 1979. On the expected value of a random assignment problem. SIAM J. Comput. 8 440-442.
21. Yedidia, J., W. Freeman, Y. Weiss. 2000. Generalized belief propagation. Technical Report TR-2000-26, Mitsubishi Electric Research Laboratories, Cambridge, MA.