利用主元一致性分解求解函数型CSP
Using Pivot Consistency to Decompose and Solve Functional CSPs
摘要：
为了提高约束满足问题的搜索效率，人们进行了大量的研究，其中有的利用了约束网络的结构特性，有的考虑了约束的语义特性，一般假设所有的约束都具有给定的性质.在本文中，我们提出了一种新的分解方法，受益于功能约束（不是双射约束）的语义属性和网络的结构属性;此外，并不是所有的约束都需要功能。我们证明了在一定条件下，可以保证解的存在性。我们首先描述一个特定的子集的变量，我们命名为根集。然后，我们引入枢轴一致性，一个新的局部一致性，这是一个弱形式的路径一致性，可以在O（n^2d^2）的复杂度实现（而不是O（n^3d^3）的路径一致性），我们提出了相关的性质;特别地，我们证明了根集的任何一致实例化都可以线性扩展到解，这导致了上述通过分解功能CSP来求解的新方法的提出。
英文摘要：
Many studies have been carried out in order to increase the search efficiency of constraint satisfaction problems; among them, some make use of structural properties of the constraint network; others take into account semantic properties of the constraints, generally assuming that all the constraints possess the given property. In this paper, we propose a new decomposition method benefiting from both semantic properties of functional constraints (not bijective constraints) and structural properties of the network; furthermore, not all the constraints need to be functional. We show that under some conditions, the existence of solutions can be guaranteed. We first characterize a particular subset of the variables, which we name a root set. We then introduce pivot consistency, a new local consistency which is a weak form of path consistency and can be achieved in O(n^2d^2) complexity (instead of O(n^3d^3) for path consistency), and we present associated properties; in particular, we show that any consistent instantiation of the root set can be linearly extended to a solution, which leads to the presentation of the aforementioned new method for solving by decomposing functional CSPs.
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