Comparative genomics is an important tool to better understand the different between species. Several methods exist to compare two genomes such that the computation of (dis)similarities' measures. In this work, we study three measures : numbers of adjacencies, of breakpoints and of common intervals. In presence of duplicated genes or when the gene order is only partially known, calculate these measures is a NP-hard problem. In first, we want to compute the numbers of adjacencies and breakpoints for three models (exemplar, intermediate, maximum) between two genomes with duplications. To get an exact result, we express these problems by pseudo-boolean programs. Thus, we can use the solver CPLEX, efficient for this study. Thanks a experimentation with 12 genomes of γ-proteobacteria, we get enough results to: compare the both measures and the 3 models and evaluate heuristics. In particular, we propose heuristics (based on a search for longest common subsequence) giving very good results. In parallel, we have established for different computational problems measures between two genomes with duplication, whether it exists a polynomial approximation. Secondly, we calculate the number of adjacencies and common intervals between two partial orders (with the possibility that one order is total). We use a programming approach pseudo-Boolean too and an other solver, efficient for this study: minisat+. Using nearly 800 simulated genomes, we study the influence of parameters associated with partial orders and we compare the two measures studied.
