Cost Function Networks (aka Weighted CSP) allow to model a variety of problems, such as optimization of deterministic and stochastic graphical models including Markov random Fields and Bayesian Networks. Solving cost function networks is thus an important problem for deterministic and probabilistic reasoning. This paper focuses on local consistencies which define essential tools to simplify Cost Function Networks, and provide lower bounds on their optimal solution cost. To strengthen arc consistency bounds, we follow the idea of triangle-based domain consistencies for hard constraint networks (path inverse consistency, restricted or max-restricted path consistencies), describe their systematic extension to cost function networks, study their relative strengths, define enforcing algorithms, and experiment with them on a large set of benchmark problems. On some of these problems, our improved lower bounds seem necessary to solve them.

中文翻译：

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成本函数网络的基于三角形的一致性

成本函数网络（又称加权CSP）可以对各种问题进行建模，例如确定性和随机图形模型的优化，包括马尔可夫随机场和贝叶斯网络。因此，求解成本函数网络是确定性和概率性推理的重要问题。本文关注于本地一致性，这些一致性定义了简化成本函数网络的基本工具，并为其最佳解决方案成本提供了下限。为了加强圆弧一致性边界，我们遵循硬约束网络（路径逆一致性，受限或最大受限路径一致性）的基于三角形的域一致性的思想，描述其对成本函数网络的系统扩展，研究其相对强度，定义执行力算法，并对它们进行大量基准测试。在其中一些问题上，我们有必要改善下限以解决这些问题。