一类极大易处理的软约束
A Maximal Tractable Class of Soft Constraints
摘要：
人工智能的许多研究人员开始探索使用软约束来表达一组（可能冲突的）问题需求。软约束是定义在一组变量上的函数，它将一些期望性度量与这些变量的每个可能的值组合相关联。然而，到目前为止，找到软约束集合的最优解的计算复杂性的关键问题很少受到关注。在本文中，我们确定了一类软二元约束的问题，找到最优解是听话的。换句话说，我们表明，对于任何给定的一组这样的约束，存在一个多项式时间的算法来确定具有最佳的整体组合的可取性措施的分配。这个易于处理的类包括许多常见的软约束，如“尽可能接近”或“尽可能快”，以及明确的约束，如“大于”。最后，我们表明，这个听话的类是最大的，在这个意义上说，增加任何其他形式的软二进制约束，这是不是在类中产生的一类问题，这是NP-硬。
英文摘要：
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which associates some measure of desirability with each possible combination of values for those variables. However, the crucial question of the computational complexity of finding the optimal solution to a collection of soft constraints has so far received very little attention. In this paper we identify a class of soft binary constraints for which the problem of finding the optimal solution is tractable. In other words, we show that for any given set of such constraints, there exists a polynomial time algorithm to determine the assignment having the best overall combined measure of desirability. This tractable class includes many commonly-occurring soft constraints, such as 'as near as possible' or 'as soon as possible after', as well as crisp constraints such as 'greater than'. Finally, we show that this tractable class is maximal, in the sense that adding any other form of soft binary constraint which is not in the class gives rise to a class of problems which is NP-hard.
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