单交叉实施
Single-crossing Implementation
摘要：
如果当我们从左到右扫描选民列表时，每对候选人的相对顺序最多改变一次，则在有限候选人集合上的选举被称为单交叉。这种选举有许多吸引人的特性：例如，他们的多数关系是传递的，他们承认有效的算法的问题是NP-困难的一般。如果一个给定的选举不是单交叉的，重要的是要了解是什么障碍，阻止它有这个属性。在本文中，我们提出了一个选举和图形之间的映射，为我们提供了一个方便的编码这样的障碍。这种映射使我们能够使用图论的工具箱来分析检测几乎单交叉选举的复杂性，即，可以通过少量修改进行单交叉的选举。
英文摘要：
An election over a finite set of candidates is called single-crossing if, as we sweep through the list of voters from left to right, the relative order of every pair of candidates changes at most once. Such elections have many attractive properties: e.g., their majority relation is transitive and they admit efficient algorithms for problems that are NP-hard in general. If a given election is not single-crossing, it is important to understand what are the obstacles that prevent it from having this property. In this paper, we propose a mapping between elections and graphs that provides us with a convenient encoding of such obstacles. This mapping enables us to use the toolbox of graph theory in order to analyze the complexity of detecting nearly single-crossing elections, i.e., elections that can be made single-crossing by a small number of modifications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
