On the exactness of the cavity method for weighted b-matchings on arbitrary graphs and its relation to linear programs

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2008, Issue 6, 2008, Pages

  Bayati, Mohsen ^a   Borgs, Christian ^a   Chayes, Jennifer ^a   Zecchina, Riccardo ^b  

^a MICROSOFT RESEARCH   (United Kingdom)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

Analysis of algorithms; Exact results; Message passing algorithms

Indexed keywords

EID: 47649086145     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2008/06/L06001     Document Type: Article

References (24)

1. Mezard M and Zecchina R 2002 Random K-satisfiability: from an analytic solution to a new efficient algorithm Phys. Rev. E 66 056126
2. Braunstein A, Mezard M and Zecchina R 2005 Survey propagation: an algorithm for satisfiability Random Struct. Algorithms 27 201
3. Braunstein A, Mulet R, Pagnani A, Weigt M and Zecchina R 2003 Phys. Rev. E 68 036702
4. Braunstein A and Zecchina R 2004 J. Stat. Mech. P06007
5. Sanghavi S, Malioutov D and Willsky A 2007 Linear programming analysis of loopy belief propagation for weighted matching Proc. NIPS Conf. (Vancouver)
6. Bayati M, Shah D and Sharma M 2008 Max-product for maximum weight matching: convergence, correctness, and LP duality IEEE Trans. Inf. Theor. 54 1241
7. Bayati M, Shah D and Sharma M 2005 Maximum weight matching via max-product belief propagation Proc. Int. Symp. on Information Theory p1763 (preliminary version)
8. Huang B and Jebara T 2007 Loopy belief propagation for bipartite maximum weight b-matching Proc. Artif. Intell. Stat. (AISTATS) Conf.
9. Gerards A 1995 Matching Hand book of Operation Research and Management Science vol 7 (Amsterdam: North-Holland) chapter 3 p135
10. Pulleyblank W 1995 Matchings and extensions Handbook of Combinatorics vol 1 (Amsterdam: North-Holland) chapter 3 p179
11. Mezard M and Parisi G 1986 Mean-field equations for the matching and travelling salesman problems Europhys. Lett. 2 913
12. Aldous D 2001 The zeta (2) limit in the random assignment problem Random Struct. Algorithms 18 381
13. Feldman J, Wainwright M and Karger D 2005 Using linear programming to decode binary linear codes IEEE Trans. Inf. Theory 51 954
14. Vontobel P O and Koetter R 2004 On the relationship between linear programming decoding and min-sum algorithm decoding Proc. ISITA (Parma, Oct. 2004) p991
15. Vontobel P O and Koetter R 2003 Graph covers and iterative decoding of finite-length codes Proc. 3rd International Symposium on Turbo Codes and Related Topics (Brest) pp75-82 [cs.IT/0512078]
16. Wainwright M, Jaakkola T and Willsky A 2005 MAP estimation via agreement on trees: message-passing and linear programming IEEE Trans. Inf. Theory 51 3697
17. Weiss Y, Yanover C and Meltzer T 2007 MAP estimation, linear programming and belief propagation with convex free energies UAI
18. Moallemi C and Van Roy B 2007 A message-passing paradigm for resource allocation Preprint available at: http://www.moallemi.com/ciamac/papers/ra-2007. pdf
19. Bayati M, Shah D and Sharma M 2006 A simpler max-product maximum weight matching algorithm and the auction algorithm Proc. IEEE Int. Symp. on Information Theory pp557-61
20. Bertsekas D P 1988 The auction algorithm: a distributed relaxation method for the assignment problem Ann. Oper. Res. 14 105
21. Gamarnik D, Nowicki T and Swirscsz G 2005 Maximum weight independent sets and matchings in sparse random graphs. Exact results using the local weak convergence method Random Struct. Algorithms 28 76
22. Zdeborov L and Mézard M 2006 The number of matchings in random graphs J. Stat. Mech.
23. Bayati M, Borgs C, Chayes J and Zecchina R 2007 Belief-propagation for weighted b-matchings on arbitrary graphs and its relation to linear programs with integer solutions Preprint 0709.1190v2
24. Sanghavi S 2007 Equivalence of LP relaxation and max-product for weighted matching in general graphs IEEE Information Theory Workshop (Sept. 2007) Preprint (preliminary version) 0705.0760