Abstract
Two models of nearly balanced random constraint satisfaction problems, called Model NB and UB respectively, are defined in this paper. By nearly balanced it means that most variables appear in the same number of constraints. Exact satisfiability thresholds for these models are proven, which are of the same values as that for Model RB. Experiments on random instances around the thresholds for these three models are conducted. The results show that these balanced models are much harder to solve than their unbalanced counterpart.
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Acknowledgments
We thank Prof. Ke Xu for suggestions on doing this work and for many helpful discussions. This work was partially supported by Natural Science Foundation of China (Grant Nos. 61370052 and 61370156) and Fundamental Research Funds for the Central Universities (Grant No. FRF-TP-16-065A1).
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Liu, T., Wang, C., Xu, W. (2018). Balanced Random Constraint Satisfaction: Phase Transition and Hardness. In: Chen, J., Lu, P. (eds) Frontiers in Algorithmics. FAW 2018. Lecture Notes in Computer Science(), vol 10823. Springer, Cham. https://doi.org/10.1007/978-3-319-78455-7_18
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