As part of our effort to construct a physical map of the genome of the fission yeast Schizosaccharomyces pombe, we have made theoretical predictions for the progress expected, as measured by the expected length fraction of island coverage and by the expected properties of the anchored islands such as the number and the size of islands. Our experimental strategy is to construct a random clone library and screen the library for clones having unique sequence at both ends. This scheme is essentially the same as the clone-limited double sequence-tagged-site selection scheme which was used in a computer simulation by Palazzolo et al. [Palazzolo, M. J., Sawyer, S. A., Martin, C. H., Smoller, D. A. & Hartl, D. L. (1991) Proc. Natl. Acad. Sci. USA 88, 8034-8038]. Both simulation and ongoing experiments in our laboratory have shown that the nonrandom anchoring method is far superior to random anchoring. In this paper, we propose a theoretical model to explain the simulated data and the experimental data.