An EM-type Algorithm for Ordered Restriction Map Alignment

Constructing restriction maps is one of the important steps towards the determination of DNA sequences. Recently, the single-molecule approaches to constructing restriction maps, such as Optical Mapping by D. Schwartz et al., have developed. In practice, with the single-molecule approach like Optical Mapping, the identification of the restriction sites is complicated by several error factors due to resolving power of biological experiments. The ordered restriction map alignment problem is a problem to estimate the actual restriction sites from many imprecise copies of map from single molecule. In this paper, we formulate the problem on the basis of the statistical maximum likelihood estimate, and propose a new efficient local search algorithm for this problem, by applying the Expectation-Maximization (EM) algorithm along with the concept of two-clustering. Our algorithm works well for a lot of sets of simulated data, some of which we believe more difficult than the actual cases.