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arXiv 1406.3124cs.AIcs.CCcs.DS
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约束满足与推理中预处理的保证与限制

Guarantees and Limits of Preprocessing in Constraint Satisfaction and Reasoning

UNSW Australia（新南威尔士大学）；NICTA（澳大利亚国家信息与通信技术研究院）；Vienna University of Technology（维也纳工业大学）

Serge Gaspers, Stefan Szeider

备注：
arXiv admin note: substantial text overlap with arXiv:1104.2541, arXiv:1104.5566
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摘要：

我们提出了第一个理论分析的权力多项式时间预处理的重要组合问题，从各个领域的人工智能。我们考虑的问题从约束满足，全局约束，可满足性，非单调和贝叶斯推理下的结构限制。所有这些问题都涉及两个任务：（i）识别输入中的结构，以满足约束的要求，以及（ii）使用识别的结构来有效地解决推理任务。我们表明，对于大多数考虑的问题，任务（一）承认一个多项式时间预处理的问题内核，其大小是多项式的结构问题参数的输入，相比之下，任务（二）不承认这样的减少到一个问题内核的多项式大小，受复杂性理论假设。作为一个值得注意的例外，我们表明，AtMost-NValue约束的一致性问题承认一个多项式核组成的二次变量和域值。我们的研究结果提供了一个坚实的最坏情况下的保证和理论边界的性能的多项式时间预处理算法所考虑的问题。

英文摘要：

We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability, Nonmonotonic and Bayesian Reasoning under structural restrictions. All these problems involve two tasks: (i) identifying the structure in the input as required by the restriction, and (ii) using the identified structure to solve the reasoning task efficiently. We show that for most of the considered problems, task (i) admits a polynomial-time preprocessing to a problem kernel whose size is polynomial in a structural problem parameter of the input, in contrast to task (ii) which does not admit such a reduction to a problem kernel of polynomial size, subject to a complexity theoretic assumption. As a notable exception we show that the consistency problem for the AtMost-NValue constraint admits a polynomial kernel consisting of a quadratic number of variables and domain values. Our results provide a firm worst-case guarantees and theoretical boundaries for the performance of polynomial-time preprocessing algorithms for the considered problems.

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