Results from physical mapping projects have recently been reported for the genomes of Escherichia coli, Saccharomyces cerevisiae, and Caenorhabditis elegans, and similar projects are currently being planned for other organisms. In such projects, the physical map is assembled by first "fingerprinting" a large number of clones chosen at random from a recombinant library and then inferring overlaps between clones with sufficiently similar fingerprints. Although the basic approach is the same, there are many possible choices for the fingerprint used to characterize the clones and the rules for declaring overlap. In this paper, we derive simple formulas showing how the progress of a physical mapping project is affected by the nature of the fingerprinting scheme. Using these formulas, we discuss the analytic considerations involved in selecting an appropriate fingerprinting scheme for a particular project.