Island length distribution in genome sequencing

We consider the general problem of constructing a physical map of a genome by welding islands of overlapping clones. Both distribution of clone length and non-uniform probability of overlap detection are taken into account, the latter restricted to the Markov case in which only the location of the end of the developing island is required. Exact results for the distribution of island length are obtained in the special cases of fixed clone length or rigid overlap criterion, and mean and variance for the general situation. Determination of ocean length distribution permits island number and contig number distributions to be found as well.