The notion of arc consistency plays a central role in constraint satisfaction. It is known that the notion of local consistency can be extended to constraint optimisation problems defined by soft constraint frameworks based on an idempotent cost combination operator. This excludes non idempotent operators such as + which define problems which are very important in practical applications such as Max-CSP, where the aim is to minimize the number of violated constraints. In this paper, we show that using a weak additional axiom satisfied by most existing soft constraints proposals, it is possible to define a notion of soft arc consistency that extends the classical notion of arc consistency and this even in the case of non idempotent cost combination operators. A polynomial time algorithm for enforcing this soft arc consistency exists and its space and time complexities are identical to that of enforcing arc consistency in CSPs when the cost combination operator is strictly monotonic (for example Max-CSP). A directional version of arc consistency is potentially even stronger than the non-directional version, since it allows non local propagation of penalties. We demonstrate the utility of directional arc consistency by showing that it not only solves soft constraint problems on trees, but that it also implies a form of local optimality, which we call arc irreducibility.
A Generalized Arc-Consistency Algorithm for a Class of Counting Constraints: Revised Edition that Incorporates One Correction
Mines-Nantes（南特矿业学院）；LINA UMR CNRS 6241（法国国家科学研究中心LINA联合研究单元（UMR 6241））
本文引入了SEQ BIN元约束，并根据其性质，提出了一种实现广义弧一致性的多时间算法。SEQ BIN可用于编码计数约束，如CHANGE、SMOOTH或INCREAS- ING NVALUE。对于其中的一些约束和它们的一些变体，GAC可以在域大小的总和中以线性的时间和空间复杂度来执行，这改进或等于文献中最好的已知结果。
Multiagent Simple Temporal Problem: The Arc-Consistency Approach
Centre for Quantum Software and Information, FEIT, University of Technology Sydney（悉尼科技大学 FEIT 量子软件与信息中心）；UTS-AMSS Joint Research Laboratory, AMSS, Chinese Academy of Sciences（中国科学院数学与系统科学研究院 UTS-AMSS 联合研究实验室）
