We present a simple and efficient method for constructing high resolution physical maps of large regions of genomic DNA based upon sampled sequencing. The physical map is constructed by ordering high density cosmid contigs and determining a sequence fragment from each end of every clone. The resulting map, which contains 30-50% of the complete DNA sequence, allows the identification of many genes and makes possible PCR amplification of virtually any part of the genome. We apply this strategy to the automated analysis of the genome of the primitive eukaryote Giardia lamblia and evaluate its applicability to the physical mapping and DNA sequencing of the human genome.