Algorithmic and combinatorial problems inspired by comparative genomics.

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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.**