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## Section: New Results

### Genomic rearrangements

• Within the context of the PhD of A. Thomas:

• We designed an algorithm for finding the minimal number of block interchanges required to transform a duplicated linear genome into a tandem duplicated linear genome. We provide a formula for the distance as well as a polynomial time algorithm for the sorting problem. This work was published in the conference Bioinformatics [13] .

• We explored a new problem concerning tandem halving, that is reconstructing a non-duplicated ancestor to a partially duplicated genome in a model where duplicated content is caused by several tandem duplications. We provide a distance in $O\left(n\right)$ time and a scenario in $O\left({n}^{2}\right)$ time. We considered several problems related to multiple tandem reconstruction and proved that the simpliest of reconstructing 2 tandems is NP-hard. This work was published in the conference WABI 2012 [14] .

• In the context of ancestral genome reconstruction, we designed an algorithm for the identification of Minimal Conflicting Sets (MCS) rows in a biological binary matrix. We provided a $O\left({n}^{2}{m}^{2}+n{m}^{7}\right)$ time algorithm, largely improving the up-to-date best algorithm in $O\left({m}^{6}{n}^{5}{\left(m+n\right)}^{2}log\left(m+n\right)\right)$ time. This work was published in the conference CPM 2012 [11] .

• In the context of the comparison of sets of alternative gene transcripts, we designed a general framework to compare sets of transcripts that are transcribed from orthologous loci of several species. The model is based on the construction of a common reference sequence, and on annotations that allow the reconstruction of ancestral sequences, the identification of conserved events, and the inference of gains and losses of donor/acceptors sites, exons, introns and transcripts. This work was published in the conference ISBRA 2012 [12] .