Bounding the scaling window of random constraint satisfaction problems

Jing Shen () and Yaofeng Ren
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Jing Shen: Naval University of Engineering
Yaofeng Ren: Naval University of Engineering

Journal of Combinatorial Optimization, 2016, vol. 31, issue 2, No 20, 786-801

Abstract: Abstract The model $$k$$ k -CSP is a random CSP model with moderately growing arity $$k$$ k of constraints. By incorporating certain linear structure, $$k$$ k -CSP is revised to a random linear CSP, named $$k$$ k -hyper- $${\mathbb F}$$ F -linear CSP. It had been shown theoretically that the two models exhibit exact satisfiability phase transitions when the constraint density $$r$$ 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 $$n$$ n . A series of experimental studies are carried out to illustrate the scaling window of the model $$k$$ k -CSP.

Keywords: Constraint satisfaction problem; Phase transition; Finite-size scaling analysis (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-014-9789-y

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