scholarly journals Random Constraint Satisfaction Problems

2009 ◽  
Vol 9 ◽  
pp. 32-37 ◽  
Author(s):  
Amin Coja-Oghlan
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Random Constraint Satisfaction Problems

The replica symmetric phase of random constraint satisfaction problems

2019 ◽  
Vol 29 (3) ◽  
pp. 346-422
Author(s):  
Amin Coja-Oghlan ◽  
Tobias Kapetanopoulos ◽  
Noela Müller
Keyword(s):  
Phase Transition ◽  
Constraint Satisfaction ◽  
Broad Class ◽  
Constraint Satisfaction Problems ◽  
Precise Location ◽  
Combinatorial Structures ◽  
Substantial Impact ◽  
Long Range Correlations ◽  
Symmetric Phase ◽  
Random Constraint Satisfaction Problems

AbstarctRandom constraint satisfaction problems play an important role in computer science and combinatorics. For example, they provide challenging benchmark examples for algorithms, and they have been harnessed in probabilistic constructions of combinatorial structures with peculiar features. In an important contribution (Krzakala et al. 2007, Proc. Nat. Acad. Sci.), physicists made several predictions on the precise location and nature of phase transitions in random constraint satisfaction problems. Specifically, they predicted that their satisfiability thresholds are quite generally preceded by several other thresholds that have a substantial impact both combinatorially and computationally. These include the condensation phase transition, where long-range correlations between variables emerge, and the reconstruction threshold. In this paper we prove these physics predictions for a broad class of random constraint satisfaction problems. Additionally, we obtain contiguity results that have implications for Bayesian inference tasks, a subject that has received a great deal of interest recently (e.g. Banks et al. 2016, Proc. 29th COLT).

scholarly journals CRITICALITY AND HETEROGENEITY IN THE SOLUTION SPACE OF RANDOM CONSTRAINT SATISFACTION PROBLEMS

2010 ◽  
Vol 24 (18) ◽  
pp. 3479-3487 ◽  
Author(s):  
HAIJUN ZHOU
Keyword(s):  
Constraint Satisfaction ◽  
Spin Glasses ◽  
Solution Space ◽  
Threshold Value ◽  
Critical Value ◽  
Constraint Satisfaction Problems ◽  
Model Systems ◽  
Dynamical Heterogeneity ◽  
Ergodicity Breaking ◽  
Random Constraint Satisfaction Problems

Random constraint satisfaction problems are interesting model systems for spin-glasses and glassy dynamics studies. As the constraint density of such a system reaches certain threshold value, its solution space may split into extremely many clusters. In this work we argue that this ergodicity-breaking transition is preceded by a homogeneity-breaking transition. For random K-SAT and K-XORSAT, we show that many solution communities start to form in the solution space as the constraint density reaches a critical value αcm, with each community containing a set of solutions that are more similar with each other than with the outsider solutions. At αcm the solution space is in a critical state. The connection of these results to the onset of dynamical heterogeneity in lattice glass models is discussed.

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