全局约束的核

摘要：

Bessiere等人（AAAI'08）表明，当某些自然问题参数很小时，可以有效地传播几个棘手的全局约束。特别是，一个全局约束的完全传播是固定参数的易处理的k -域中的孔的数量-只要绑定的一致性可以在多项式时间内执行;这适用于全局约束AtMost-NValue和扩展全局基数（EGC）。在本文中，我们延长这条线的研究，并介绍了减少到一个问题的核心，参数化复杂性的一个关键概念的概念，到该领域的全局约束。特别是，我们证明了AtMost-NValue约束的一致性问题允许线性时间减少到O（k^2）变量和域值的等价实例。这个小内核可以用来加速NValue约束的完全传播。我们对比这一结果表明，EGC约束的一致性问题不承认减少到一个多项式问题的内核，除非多项式层次崩溃。

英文摘要：

Bessiere et al. (AAAI'08) showed that several intractable global constraints can be efficiently propagated when certain natural problem parameters are small. In particular, the complete propagation of a global constraint is fixed-parameter tractable in k - the number of holes in domains - whenever bound consistency can be enforced in polynomial time; this applies to the global constraints AtMost-NValue and Extended Global Cardinality (EGC). In this paper we extend this line of research and introduce the concept of reduction to a problem kernel, a key concept of parameterized complexity, to the field of global constraints. In particular, we show that the consistency problem for AtMost-NValue constraints admits a linear time reduction to an equivalent instance on O(k^2) variables and domain values. This small kernel can be used to speed up the complete propagation of NValue constraints. We contrast this result by showing that the consistency problem for EGC constraints does not admit a reduction to a polynomial problem kernel unless the polynomial hierarchy collapses.

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