Kemeny秩集结的多样性：一种参数化方法
Diversity in Kemeny Rank Aggregation: A Parameterized Approach
摘要：
在其最传统的设置中，优化理论的主要关注点是为给定计算问题的实例寻找最优解。最近人工智能研究的一个趋势，称为解决方案多样性，集中在最优性概念的发展，可能更适合于主观性是必不可少的设置。我们的想法是，而不是针对输出一个单一的最优解的算法的发展，目标是研究算法，输出一个小的足够好的解决方案，是足够不同的彼此。通过这种方式，用户有机会选择最适合当前上下文的解决方案。它还显示了解决方案空间的丰富性。当与参数化复杂性理论的技术相结合时，解决方案多样性的范式提供了一个强大的算法框架来解决实际相关的问题。在这项工作中，我们调查的影响，这种组合在该领域的Kemeny秩聚合，一个研究的问题，躺在交叉点的秩序理论和社会选择理论，也在该领域的秩序理论本身。特别是，我们表明，Kemeny秩聚合问题是固定参数易于处理的自然参数提供自然形式化的概念的多样性和一个足够好的解决方案的概念。我们的主要结果工作时，考虑到传统的设置聚集在线性有序的选票，并在更一般的设置，其中选票是部分有序的。
英文摘要：
In its most traditional setting, the main concern of optimization theory is the search for optimal solutions for instances of a given computational problem. A recent trend of research in artificial intelligence, called solution diversity, has focused on the development of notions of optimality that may be more appropriate in settings where subjectivity is essential. The idea is that instead of aiming at the development of algorithms that output a single optimal solution, the goal is to investigate algorithms that output a small set of sufficiently good solutions that are sufficiently diverse from one another. In this way, the user has the opportunity to choose the solution that is most appropriate to the context at hand. It also displays the richness of the solution space. When combined with techniques from parameterized complexity theory, the paradigm of diversity of solutions offers a powerful algorithmic framework to address problems of practical relevance. In this work, we investigate the impact of this combination in the field of Kemeny Rank Aggregation, a well-studied class of problems lying in the intersection of order theory and social choice theory and also in the field of order theory itself. In particular, we show that the Kemeny Rank Aggregation problem is fixed-parameter tractable with respect to natural parameters providing natural formalizations of the notions of diversity and of the notion of a sufficiently good solution. Our main results work both when considering the traditional setting of aggregation over linearly ordered votes, and in the more general setting where votes are partially ordered.
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。
