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Asymptotic properties of random regular graphs are object of extensive study in mathematics.
Solvable model of a spin-glass
D. Sherrington and S. Kirkpatrick · 1975
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Computers and intractability: A guide to the theory of NP-completeness
M. R. Garey and D. S. Johnson · 1979
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The order parameter for spin-glasses: A function on the interval 0–1
G. Parisi · 1980
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Mean-field theory of the Potts glass
D. J. Gross, I. Kanter, and H. Sompolinsky · 1985
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Application of statistical mechanics to NP-complete problems in combinatorial optimization
Y. Fu and P. W. Anderson · 1986
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Spin-Glass Theory and Beyond
M. Mézard, G. Parisi, and M. A. Virasoro · 1987
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Mean-field theory of randomly frustrated systems with finite connectivity
M. Mézard and G. Parisi · 1987
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Graph bipartitioning and the Bethe spin glass
D. Sherrington and K. Y. M Wong · 1987
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Graph bipartitioning and spin glasses on a random network of fixed finite valence
K. Y. M. Wong and D. Sherrington · 1987
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Graph optimization problems and the Potts glass
I. Kanter and H. Sompolinsky · 1987
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The isoperimetric number of random regular graphs
B. Bollobas · 1988
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Graph partitioning and dilute spin glasses: the minimum cost solution
K. Y. M. Wong, D. Sherrington, P. Mottishaw, R. Dewar, and C. DeDominicis · 1988
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On bounds of the bisection width of cubic graphs
A. V. Kostochka and L. S. Melnikov · 1992
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Recent directions in netlist partitioning – a survey
C. J. Alpert and A. B. Kahng · 1995
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A multilevel algorithm for partitioning graphs
B. A. Hendrickson and R. Leland · 1995
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Maximum cuts and largest bipartite subgraphs
S. Poljak and Z. Tuza · 1995
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Extremal Optimization and graph partitioning at the percolation threshold
S. Boettcher · 1999
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Nature’s way of optimizing
S. Boettcher and A. G. Percus · 2000
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Upper bounds on the bisection width of 3- and 4-regular graphs
B. Monien and R. Preis · 2001
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The Bethe lattice spin glass revisited
Numerical results for ground states of mean-field spin glasses at low connectivities
S. Boettcher · 2003
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The cavity method at zero temperature
M. Mézard and G. Parisi · 2003
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Constraint satisfaction by survey propagation
A. Braunstein, M. Mézard, M. Weigt, and R. Zecchina · 2003
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New Optimization Algorithms in Physics
A. Hartmann and H. Rieger, editors · 2004
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Spin glass models with ferromagnetically biased couplings on the Bethe lattice: analytic solution and numerical simulations
T. Castellani, F. Krzakala, and F. Ricci-Tersenghi · 2005
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An upper bound for the maximum cut mean value
A. Bertoni, P. Campadelli, and R. Posenato · 2006
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M. Mézard and G. Parisi · 2001
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Optimization with extremal dynamics
S. Boettcher and A. G. Percus · 2001
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Extremal Optimization for graph partitioning
S. Boettcher and A. G. Percus · 2001
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Jamming model for the extremal optimization heuristic
S. Boettcher and M. Grigni · 2002
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Bounds on the max and min bisection of random cubic and random 4-regular graphs
J. Díaz, N. Do, M. J. Serna, and N. C. Wormald · 2003
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Numerical results for ground states of spin glasses on Bethe lattices
S. Boettcher · 2003
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The Parisi formula
M. Talagrand · 2006
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Bounds on the bisection width for random d -regular graphs
J. Diaz, M. J. Serna, and N. C. Wormald · 2007
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Ising models on locally tree-like graphs
A. Dembo and A. Montanari · 2008
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The peculiar phase structure of random graph bisection
A. G. Percus, G. Istrate, B. Gonçalves, R. Z. Sumi, and S. Boettcher · 2008
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Potts glass on random graphs
F. Krzakala and L. Zdeborová · 2008
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Belief propagation for graph partitioning
P. Šulc and L. Zdeborová · 2009
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