Algorithms for Optical Mapping

Optical mapping is a novel technique for determining the restriction sites on a DNA molecule by directly observing a number of partially digested copies of the molecule under a light microscope. The problem is complicated by uncertainty as to the orientation of the molecules and by erroneous detection of cuts. In this paper we study the problem of constructing a restriction map based on optical mapping data. We give several variants of a polynomial reconstruction algorithm, as well as an algorithm that is exponential in the number of cut sites, and hence is appropriate only for small number of cut sites. We give a simple probabilistic model for data generation and for the errors and prove probabilistic upper and lower bounds on the number of molecules needed by each algorithm in order to obtain a correct map, expressed as a function of the number of cut sites and the error parameters. To the best of our knowledge, this is the first probabilistic analysis of algorithms for the problem. ..