二值域弧一致性算法用于时间约束满足问题：其计算分析及其作为解决方案搜索算法中过滤过程的用途
A binarized-domains arc-consistency algorithm for TCSPs: its computational analysis and its use as a filtering procedure in solution search algorithms
AI总结：
本文提出一种针对时间约束满足问题的二值域弧一致性算法，分析其计算性能，并作为解决方案搜索算法中的过滤机制，同时比较了不同调度器的性能。
摘要：
TCSPs (Temporal Constraint Satisfaction Problems) [Dechter et al. 1991] 通过在添加一个'世界起源'变量后消除单变量约束。在本文中，我们研究'世界起源'变量与其他变量之间的约束，作为这些其他变量的(二值化)域。基于此，我们定义了TCSPs的弧一致性概念，称为二值域弧一致性(binarized-domains Arc-Consistency, bdArc-Consistency)。我们提供了一个实现bdArc-Consistency的算法，称为bdAC-3，它是Mackworth [1977] 知名的弧一致性算法AC-3的变种。我们证明，如果一个STP是bdArc-一致且连通，即其'世界起源'变量与其他变量均不断开连接，则其二值化域是极小的。我们提供了两个多项式回溯自由的程序：一个用于从连通的bdArc-一致STP中获得解；另一个用于从bdArc-一致STP中获取不一致或在一致的情况下获得改进的连通bdArc-一致STP。然后我们展示了如何将我们的结果应用于通用TCSP求解器和基于TCSP的作业调度器。此外，本文还提供了bdAC-3与现有弧一致性算法ACSTP在STP上的实验比较；比较了三种基于TCSP的作业调度器，其中两个使用弱版本的bdAC-3作为搜索过程中的过滤程序，第三个[Schwalb and Dechter 1997]使用弱路径一致性；以及这些比较所使用的swi-prolog源代码。最后，我们还提供了一个bdAC-3的增量版本。
英文摘要：
TCSPs (Temporal Constraint Satisfaction Problems) [Dechter et al. 1991] get rid of unary constraints by binarizing them after having added an "origin of the world" variable. In this work, we look at the constraints between the "origin of the world" variable and the other variables, as the (binarized) domains of these other variables. With this in mind, we define a notion of arc-consistency for TCSPs, which we will refer to as binarized-domains Arc-Consistency, or bdArc-Consistency for short. We provide an algorithm achieving bdArc-Consistency for a TCSP, which we will refer to as bdAC-3, for it is an adaptation of Mackworth's [1977] well-known arc-consistency algorithm AC-3. We show that if an STP is bdArc-Consistent, and connected, i.e., its "origin of the world" variable is disconnected from none of the other variables, its binarized domains are minimal. We provide two polynomial backtrack-free procedures: one for the task of getting a solution from a connected bdArc-Consistent STP; the other for the task of getting, from a bdArc-Consistent STP, either that it is inconsistent or, in case of consistency, a connected bdArc-Consistent STP refinement. We then show how to use our results both in a general TCSP solver and in a TCSP-based job shop scheduler. The work also provides an experimental comparison on STPs of bdAC-3 with an existing arc-consistency algorithm, ACSTP, restricted to STPs [Kong et al. 2018]; an experimental comparison of three TCSP-based job shop schedulers, two of which use weak versions of bdAC-3 as the filtering procedure during the search, the third [Schwalb and Dechter 1997] a weak version of path-consistency; and the swi-prolog source codes used by these comparisons. Last but not least, we provide an incremental version of bdAC-3.
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