Belief propagation for graph partitioning

Journal of Physics A: Mathematical and Theoretical

Volumn 43, Issue 28, 2010, Pages

  Šulc, Petr ^a,b,c   Zdeborová, Lenka ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b NEW MEXICO CONSORTIUM   (United States)

^c CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77953776556     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/43/28/285003     Document Type: Article

References (41)

1. Kirkpatrick S, Gelatt C D Jr and Vecchi M P 1983 Optimization by simulated annealing Science 220 671-80
2. Fu Y and Anderson P W 1986 Application of statistical mechanics to NP-complete problems in combinatorial optimization J. Phys. A: Math. Gen. 19 1605-20
3. Mézard M and Parisi G 1985 Replicas and optimization J. Physique 46 771-8
4. Mézard M, Parisi G and Zecchina R 2002 Analytic and algorithmic solution of random satisfiability problems Science 297 812-5
5. Krzakala F, Montanari A, Ricci-Tersenghi F, Semerjian G and Zdeborov L 2007 Gibbs states and the set of solutions of random constraint satisfaction problems Proc. Natl Acad. Sci. USA 104 10318
6. Mézard M and Parisi G 2001 The bethe lattice spin glass revisited Eur. Phys. J. B 20 217-33 DOI:10.1007/PL00011099
7. Garey M R and Johnson D S 1979 Computers and Intractability: A Guide to The Theory of NP-Completeness (San Francisco, CA: Freeman)
8. Karypis G, Aggarwal R, Kumar V and Shekhar S 1999 Multilevel hypergraph partitioning: applications in vlsi domain IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 7 69-79
9. Pothen A 1997 Graph partitioning algorithms with applications to scientific computing Technical report Norfolk, VA, USA
10. Girvan M and Newman M E J 2002 Community structure in social and biological networks Proc. Natl Acad. Sci. USA 99 7821-6
11. Kernighan B and Lin S 1970 An efficient heuristic procedure for partitioning graphs Bell Syst. Tech. J. 49 291-307
12. Banavar J R, Sherrington D and Sourlas N 1987 Graph bipartitioning and statistical mechanics J. Phys. A: Math. Gen. 20 L1-8 DOI:10.1088/0305-4470/20/1/ 001
13. Schreiber G R and Martin O C 1999 Cut size statistics of graph bisection heuristics SIAM J. Optim. 10 231-51
14. Boettcher S and Percus A G 2001 Extremal optimization for graph partitioning Phys. Rev. E 64 026114
15. Hagen L and Kahng A B 1992 New spectral methods for ratio cut partitioning and clustering IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 11 1074-85 (Pubitemid 23555831)
16. Karypis G and Kumar V 1999 A fast and high quality multilevel scheme for partitioning irregular graphs SIAM J. Sci. Comput. 20 359-92
17. Bollobas B 1988 The isoperimetric number of random regular graphs Eur. J. Comb. 9 241-4
18. Kostochka A V and Melnikov L S 1992 On bounds of the bisection width of cubic graphs Fourth Czechoslovakian Symposium on Combinatorics, Graphs and Complexity ed J Nesetril and M Fiedler (Amsterdam: Elsevier) pp 151-4
19. Monien B and Preis R 2001 Upper bounds on the bisection width of 3- and 4-regular graphs (MFCS '01: Proc 26th Int Symposium on Mathematical Foundations of Computer Science) (London: Springer) pp 524-36 DOI:10.1007/3-540-44683-4-46
20. Díaz J, Do N, Serna M J and Wormald N C 2003 Bounds on the max and min bisection of random cubic and random 4-regular graphs Theor. Comput. Sci. 307 531-47
21. Diaz J, Serna M J and Wormald N C 2007 Bounds on the bisection width for random d-regular graphs Theor. Comput. Sci. 382 120-30 (Latin American Theoretical Informatics)
22. Percus A G, Istrate G, Goncalves B, Sumi R Z and Boettcher S 2008 The peculiar phase structure of random graph bisection J. Math. Phys. 49 (arXiv:0808.1549v2 [cond-mat.stat-mech])
23. Sherrington D and Wong K Y M 1987 Graph bipartitioning and the Bethe spin glass J. Phys. A: Math. Gen. 20 L785-91
24. Wong K Y M and Sherrington D 1987 Graph bipartitioning and spin glasses on a random network of fixed finite valence J. Phys. A: Math. Gen. 20 L793-9
25. Mézard M and Parisi G 1987 Mean-field theory of randomly frustrated systems with finite connectivity Europhys. Lett. 3 1067-74
26. Wong K Y M, Sherrington D, Mottishaw P, Dewar R and De Dominicis C 1988 Graph partitioning and dilute spin glasses: the minimum cost solution J. Phys. A: Math. Gen. 21 L99-105
27. Liao W 1988 Replica symmetric solutions of the graph-bipartitioning problem with fixed, finite valence J. Phys. A: Math. Gen. 21 427-40
28. Goldschmidt Y Y and De Dominicis C 1990 Replica symmetry breaking in the spin-glass model on lattices with finite connectivity: application to graph partitioning Phys. Rev. B 41 2184-2197
29. Mézard M and Parisi G 2003 The cavity method at zero temperature J. Stat. Phys. 111 1-34
30. Di C, Montanari A and Urbanke R 2004 Weight distributions of LDPC code ensembles: combinatorics meets statistical physics Int. Symposium on Information Theory (IEEE)
31. Mora T and Mézard M 2006 Geometrical organization of solutions to random linear Boolean equations J. Stat. Mech. 10 P10007
32. Krzakala F, Ricci-Tersenghi F and Zdeborov L 2009 Elusive glassy phase in the random field Ising model arXiv:0911.1551v1 [cond-mat.dis-nn]
33. Zdeborov L and Boettcher S 2010 A conjecture about max-cut size and bisection width in random regular graphs J. Stat. Mech. P02020 DOI:10.1088/1742-5468/2010/02/P02020
34. Yedidia J S, Freeman W T and Weiss Y 2002 Understanding belief propagation and its generalizations Exploring Artificial Intelligence in the New Millennium (San Francisco, CA: Morgan Kaufmann) pp 236-239
35. Mézard M and Montanari A 2009 Physics, Information, Computation (Oxford: Oxford University Press)
36. Sherrington D and Kirkpatrick S 1975 Solvable model of a spin-glass Phys. Rev. Lett. 35 1792-6
37. Parisi G 1980 The order parameter for spin-glasses: a function on the interval 0-1 J. Phys. A: Math. Gen. 13 1101-12
38. de Almeida J R L and Thouless D J 1978 Stability of the Sherrington-Kirkpatrick solution of a spin-glass model J. Phys. A: Math. Gen. 11 983-90
39. Zdeborov L 2009 Statistical physics of hard optimization problems Acta Phys. Slovaca 59 169-303
40. Franz S, Leone M, Ricci-Tersenghi F and Zecchina R 2001 Exact solutions for diluted spin glasses and optimization problems Phys. Rev. Lett. 87 127209
41. Chavas J, Furtlehner C, Mézard M and Zecchina R 2005 Survey-propagation decimation through distributed local computations J. Stat. Mech.: Theory Exp. 2005 P11016