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Given a graph $G$ of degree $k$ over $n$ vertices, we consider the problem of computing a near maximum cut or a near minimum bisection in polynomial time.
The Parisi formula
Michel Talagrand · 2006
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A proof of Alon’s second eigenvalue conjecture and related problems
Joel Friedman · 2008
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A conjecture on the maximum cut and bisection width in random regular graphs
Lenka Zdeborová and Stefan Boettcher · 2010
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The dynamics of message passing on dense graphs, with applications to compressed sensing
Mohsen Bayati and Andrea Montanari · 2011
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Combinatorial approach to the interpolation method and scaling limits in sparse random graphs
Mohsen Bayati, David Gamarnik, and Prasad Tetali · 2013
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Right-convergence of sparse random graphs
David Gamarnik · 2014
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The Parisi formula has a unique minimizer
Antonio Auffinger and Wei-Kuo Chen · 2015
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Ramanujan graphings and correlation decay in local algorithms
Ágnes Backhausz, Balázs Szegedy, and Bálint Virág · 2015
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Invariant gaussian processes and independent sets on regular graphs of large girth
Endre Csóka, Balázs Gerencsér, Viktor Harangi, and Bálint Virág · 2015
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A dynamic programming approach to the Parisi functional
Aukosh Jagannath and Ian Tobasco · 2016
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The interpolation method for random graphs with prescribed degrees
Justin Salez · 2016
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Parisi formula for the ground state energy in the mixed p p -spin model
Antonio Auffinger and Wei-Kuo Chen · 2017
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Variational representations for the Parisi functional and the two-dimensional Guerra–Talagrand bound
Wei-Kuo Chen · 2017
Cited alongside, same era.
Extremal cuts of sparse random graphs
Amir Dembo, Andrea Montanari, and Subhabrata Sen · 2017
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How well do local algorithms solve semidefinite programs?
Zhou Fan and Andrea Montanari · 2017
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Convergence of maximum bisection ratio of sparse random graphs
Brice Huang · 2018
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Probability: theory and examples
Rick Durrett · 2019
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The Ising antiferromagnet and max cut on random regular graphs
Amin Coja-Oghlan, Philipp Loick, Balázs F Mezei, and Gregory B Sorkin · 2020
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Optimization of Mean-field Spin Glasses
Ahmed El Alaoui, Andrea Montanari, and Mark Sellke · 2021
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Joao Basso, Edward Farhi, Kunal Marwaha, Benjamin Villalonga, and Leo Zhou · 2021
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Factors of IID on Trees
Russell Lyons · 2017
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On the Max-Cut of Sparse Random Graphs
David Gamarnik and Quan Li · 2018
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Andrea Montanari · 2021
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Optimizing Mean Field Spin Glasses with External Field
Mark Sellke · 2021
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Classical algorithms and quantum limitations for maximum cut on high-girth graphs
Boaz Barak and Kunal Marwaha · 2022
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