Combinatorial Objects in Bio-Algorithmics: Related problems and complexities

The aim of this habilitation is to exhibit my contributions in several area of Bio-Algorithmics. Rather than an exhaustive presentation of my works, I have made the choice of presenting results we obtained with collaborators on a representative subset of the problems I have been involved in since 2005. For ease of readability, I will regroup the results obtained according to the biological problems: i) RNA structures comparison, ii) Genomes comparison and iii) Pattern matching in biological networks and their respective combinatorial objects: i) Arc-annotated sequences, ii) Permutations and Sequences and iii) Graphs. More precisely, The first part will be devoted to the Arc-Annotated Sequences that are used in RNA structure comparison. We will focus on five problems that we investigated: LAPCS, APS, MAPCS, EDIT and ALIGN. In the second part, we will consider the two main research area related to comparative genomics we were involved in: gene clusters detection and (dis)similarity measures computation -- which rely on permutation and string representations. Finally, we will present some results that were obtained mainly during the PhD of Florian Sikora that I co-supervised.

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