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.
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Acknowledgments
The authors are grateful to Professor Ke Xu from Beihang University for helpful discussions. Many thanks are given to the anonymous reviewers for their valuable comments. This work is supported by the National Natural Science Foundation of China (Grant No. 11171370, 61370052, 61402516).
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Shen, J., Ren, Y. Bounding the scaling window of random constraint satisfaction problems. J Comb Optim 31, 786–801 (2016). https://doi.org/10.1007/s10878-014-9789-y
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DOI: https://doi.org/10.1007/s10878-014-9789-y