Optical mapping generates an ordered restriction map of a DNA molecule, that is, an ordered enumeration of the restriction sites along with the estimated lengths of the restriction fragments between consecutive restriction sites and various statistics, which model the errors in estimating the restriction fragment lengths and due to unrepresented and misrepresented restriction sites in the map. They have applications in improving the accuracy and algorithmic efficiency of sequence assembly, validating assembled sequences, characterizing gaps in the assembly and identifying candidates for finishing steps in a sequencing project, etc.