Algorithmic and combinatorial problems inspired by comparative genomics.

摘要：坐在理论计算机科学和数学的接口，我的研究领域涉及的算法方法和组合工具的发展受到生物学问题的启发，主要来自比较基因组学的理论问题。粗略地说，比较基因组学旨在从不同物种的基因组比较中提取信息。这些信息可能涉及基因组序列本身、基因在不同基因组中出现的顺序、小分子（如RNA）的结构等。 从大量的生物数据中提取有意义的信息的一般问题引起了许多关于组合对象的重要问题，如单词、排列、树或图。例如，排列部分编码基因组的结构。在这种情况下，开发有效的算法来操纵这些离散结构也是至关重要的。人们发现，在任何一个这些特定的背景下，许多不同的距离概念已被提出来比较相关的对象，其结果是，我们现在必须清楚地描述这些距离中的"最佳“距离。可以肯定的是，这种距离的质量测量与实现预期目标的有效算法的构建密切相关。 我的研究项目包括研究如何比较和分析这些距离的主要属性，并量化它们与给定上下文的相关性。本研究的具体结果导致新的高效算法的建设，以帮助解决与距离优化相关的几个问题。在应用背景中，距离的重要用途之一是寻找一种方法，将给定问题的一组解决方案聚合成一个共识解决方案，该解决方案突出了共同的期望特征，同时最大限度地减少分歧。我的程序的一个原始方面在于研究如何在各种情况下有效地（算法）达到这些共识解决方案。

Abstract: Sitting at the interface of theoretical computer science and mathematics, my area of research concerns the development of algorithmic approaches and combinatorial tools for theoretical problems inspired by biological problems, coming mostly from comparative genomics. Roughly speaking, comparative genomics aims at extracting information from the comparison of genomes of different species. This information may concern genomic sequences themselves, the order of appearance of genes in different genomes, the structure of small molecules (like RNA), etc. The general problem of extracting meaningful information from the resulting very large mass of biological data gives rise to many important problems on combinatorial objects such as words, permutations, trees or graphs. For instance, permutations partially encode the structure of genomes. The development of efficient algorithms for the manipulation of these discrete structures is also crucial in this context. One finds that, in any one of these specific contexts, many different notions of distances have been suggested to compare the relevant objects, with the consequence that we now have to clearly characterize the ``best'' distances among these. For sure, this quality measurement of distances is closely tied to the construction of efficient algorithms fulfilling the desired goal. My research program consists in studying how one should compare and analyze such distances with respect to their principal properties, and to quantify their relevance to a given context. Concrete results of this study lead to the construction of new efficient algorithms to help solve several problems related to distances optimization. Among important uses of distances in applied contexts one looks for a way to aggregate a set of solutions of a given problem into a consensus solution which highlights common desired features, while minimizing disagreements. One original aspect of my program rests on the study of how to efficiently (algorithmically) reach these consensus solutions in various context.