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摘要翻译：
我们考虑一种常见的对称类型，其中我们有一个具有可互换行和列的决策变量矩阵。处理这样的行和列对称性的一个简单而有效的方法是张贴对称破缺约束，如DOUBLELEX和Snakelex。我们给出了一些关于对称破缺约束的正反结果。在积极的方面，我们证明了在行数（或列数）有界的情况下以及在其他一些特殊情况下，我们可以在多项式时间内计算出行和列对称的矩阵模型中等价类的唯一表示。在消极的方面，我们证明了虽然DOUBLELEX和SNAKELEX在实践中通常是有效的，但在最坏的情况下它们可以留下大量的对称解。此外，我们还证明了完全传播DOUBLELEX是NP难的。最后我们考虑了如何打破行、列和值的对称性，修正了文献中关于组合不同对称性打破约束的安全性的一个结果。我们以DOUBLELEX和SNAKELEX在一些基准问题上留下多少对称性的第一个实验研究结束。
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英文标题：
《On The Complexity and Completeness of Static Constraints for Breaking
Row and Column Symmetry》
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作者：
George Katsirelos and Nina Narodytska and Toby Walsh
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最新提交年份：
2010
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分类信息：
一级分类：Computer Science 计算机科学
二级分类：Artificial Intelligence 人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Computer Science 计算机科学
二级分类：Computational Complexity 计算复杂度
分类描述：Covers models of computation, complexity classes, structural complexity, complexity tradeoffs, upper and lower bounds. Roughly includes material in ACM Subject Classes F.1 (computation by abstract devices), F.2.3 (tradeoffs among complexity measures), and F.4.3 (formal languages), although some material in formal languages may be more appropriate for Logic in Computer Science. Some material in F.2.1 and F.2.2, may also be appropriate here, but is more likely to have Data Structures and Algorithms as the primary subject area.
涵盖计算模型，复杂度类别，结构复杂度，复杂度折衷，上限和下限。大致包括ACM学科类F.1（抽象设备的计算）、F.2.3（复杂性度量之间的权衡）和F.4.3（形式语言）中的材料，尽管形式语言中的一些材料可能更适合于计算机科学中的逻辑。在F.2.1和F.2.2中的一些材料可能也适用于这里，但更有可能以数据结构和算法作为主要主题领域。
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英文摘要：
We consider a common type of symmetry where we have a matrix of decision variables with interchangeable rows and columns. A simple and efficient method to deal with such row and column symmetry is to post symmetry breaking constraints like DOUBLELEX and SNAKELEX. We provide a number of positive and negative results on posting such symmetry breaking constraints. On the positive side, we prove that we can compute in polynomial time a unique representative of an equivalence class in a matrix model with row and column symmetry if the number of rows (or of columns) is bounded and in a number of other special cases. On the negative side, we show that whilst DOUBLELEX and SNAKELEX are often effective in practice, they can leave a large number of symmetric solutions in the worst case. In addition, we prove that propagating DOUBLELEX completely is NP-hard. Finally we consider how to break row, column and value symmetry, correcting a result in the literature about the safeness of combining different symmetry breaking constraints. We end with the first experimental study on how much symmetry is left by DOUBLELEX and SNAKELEX on some benchmark problems.
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PDF链接：
https://arxiv.org/pdf/1007.0602
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