Section: New Results

Combinatorics of motifs and algorithms

We developed an $O\left(n\right)$-time and $O\left(n\right)$-space algorithm to compute minimal absent words. Their computation is used in sequence comparison [32] or to detect biologically significant events. For instance, in [52] , it was shown that there exist three minimal words in Ebola virus genomes which are absent from human genome. The identification of such species-specific sequences may prove to be useful for the development of both diagnosis and therapeutics. In our new contribution [21] we provided an implementation that can be executed in parallel. Experimental resuts show that excluding the indexing data structure construction time, it achieves near-optimal speed-ups. The computation on the human genome is accelerated by a factor of 10 when using 16 processors, but it consummes a huge amout of RAM. Thus we are currently working on an external memory implementation, that will provide a trade-off between space and time consumption.

Combinatorial tools have been developed to predict the length of repetitions in a random sequence. This allows to distinguish biologically significant repetitions or tune some parameters in assembly or re-sequencing algorithms. For instance, unique mappability is strongly related to the length of the repetitions. A trie profile was defined in [45] to address this issue for binary alphabets, by the means of analytic combinatorics. General alphabets, where no closed formula exist, were adressed in [24] . An alternative, and simpler, approach is derived, thatexhibits a Large deviation Principle and makes use of Lagrange multipliers. Different domains and transition phases are exhibited. It is expected that htis approach extends to a Markov model and to approximate repetitions.