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Erschienen in:
01.02.2016
Bounding the scaling window of random constraint satisfaction problems
Erschienen in: Journal of Combinatorial Optimization | Ausgabe 2/2016
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Abstract
The model \(k\)-CSP is a random CSP model with moderately growing arity \(k\) of constraints. By incorporating certain linear structure, \(k\)-CSP is revised to a random linear CSP, named \(k\)-hyper-\({\mathbb F}\)-linear CSP. It had been shown theoretically that the two models exhibit exact satisfiability phase transitions when the constraint density \(r\) is varied accordingly. In this paper, we use finite-size scaling analysis to characterize the threshold behaviors of the two models with finite problem size \(n\). A series of experimental studies are carried out to illustrate the scaling window of the model \(k\)-CSP.