This paper outlines an algorithm for whole genome order restriction optical map assembly. The algorithm can run very reliably in polynomial time by exploiting a strict limit on the probability that two maps that appear to overlap are in fact unrelated (false positives). The main result of this paper is a tight bound on the false positive probability based on a careful model of the experimental errors in the maps found in practice. Using this false positive probability bound, we show that the probability of failure to compute the correct map can be limited to acceptable levels if the input map error rates satisfy certain sharply delineated conditions. Thus careful experimental design must be used to ensure that whole genome map assembly can be done quickly and reliably.