Spaced seed design on profile HMMs for precise HTS read-mapping - efficient sliding window product on the matrix semi-group

We propose a new method and its associated algorithm to e ciently compute seed sensitivity when considering that High Throughput Sequencing reads are mapped along sub-parts of a known HMM alignment profile. This computation particularly makes sense with positioned spaced seeds. It relies on both automata theory (previous work [KNR06]) combined with a matrix product problem. Interestingly, it brings into light an interval product problem considered more than twenty years ago in [AS87], but here with a sliding window aspect : we propose an e cient algorithm to compute this sliding window set of products using a linear number of unit products on the (associative, but non commutative and non invertible) matrix semi-group. This computational scheme is implemented in the ongoing 1.06 version of Iedera which is available at http://bioinfo.lifl.fr/yass/iedera.php