2017
DOI: 10.21468/scipostphys.2.3.019
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Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems

Abstract: Random constraint satisfaction problems (CSP) have been studied extensively using statistical physics techniques. They provide a benchmark to study average case scenarios instead of the worst case one. The interplay between statistical physics of disordered systems and computer science has brought new light into the realm of computational complexity theory, by introducing the notion of clustering of solutions, related to replica symmetry breaking. However, the class of problems in which clustering has been stu… Show more

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Cited by 116 publications
(277 citation statements)
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“…At even larger values of γ, λ reaches one, indicating that the transition becomes a RFOT. This behavior is reminiscent of that of several spin glass models [56,57].…”
Section: A Glass Phase Diagramsupporting
confidence: 52%
“…At even larger values of γ, λ reaches one, indicating that the transition becomes a RFOT. This behavior is reminiscent of that of several spin glass models [56,57].…”
Section: A Glass Phase Diagramsupporting
confidence: 52%
“…Note that the same equation of eq. (42) holds exactly in the case of mean-field model of nonspherical particles [5,9] and the spherical particles slightly above the jamming transition point, where δz ∼ p 1/2 [23]. For the force distribution P (f ), one can apply a similar argument, and it has been shown that…”
Section: General Scaling Form Of the Distribution Functions Near Isosmentioning
confidence: 85%
“…This suggests that one can extend the perceptron model studied in Ref. [32,46], by replacing the effective diameter σ by a fluctuating one [45]…”
Section: The Polydisperse Perceptron Modelmentioning
confidence: 99%
“…. After a standard but slightly lengthy procedure (see Appendix A and [46]), one obtains the saddle point condition for x(q) as the solution of:…”
Section: Free Energy and Thermodynamic Quantitiesmentioning
confidence: 99%