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An upper (lower) bound for Max (Min) CSP

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Abstract

The random constraint satisfaction problem (CSP) instances generated by Model RB have been widely used in the field of CSP and have some nice features. In this paper, we consider two optimization versions of CSP, i.e., the maximum constraint satisfaction problem (Max-CSP) and the minimum satisfaction problem (Min-CSP) of Model RB. The problem of the Max-CSP is how to find an assignment to all the variables such that the maximum number of constraints are satisfied and the problem of Min-CSP is how to find an assignment to all the variables such that the minimum number of constraints are satisfied. We use the first moment method to prove that when r > 2α(1/p−1) (or p > 2α/(2α+r)), an upper bound of Max-CSP can be derived. Similarly, we can prove that when r > 2α(1/p−1) (or p > 2α/(2α + r)), a lower bound of Min-CSP can be derived.

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Authors and Affiliations

  1. School of Electronics Engineering and Computer Science, Peking University, Beijing, 100871, China

    Ping Huang

  2. School of Computer Science and Information Technology, Northeast Normal University, Changchun, 130117, China

    Ping Huang & MingHao Yin

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  1. Ping Huang
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  2. MingHao Yin
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Correspondence to MingHao Yin.

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Huang, P., Yin, M. An upper (lower) bound for Max (Min) CSP. Sci. China Inf. Sci. 57, 1–9 (2014). https://doi.org/10.1007/s11432-013-5052-x

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