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The DNA of an organism can be digested into smaller fragments, stored individually as clones in phage, for example, to create a clone library, and retrieved later, when needed. The original ordering of fragments is lost in the process of creating the library. Hence, it is important to be able to place clones in order according to their position along chromosome(s), and this process is referred to as "in vitro reconstruction" or "contig mapping" of an organismal genome. Clones in the phage library can be assigned binary call numbers by scoring each clone for hybridization (0 or 1) with a battery of short manufactured DNA sequences called synthetic oligonucleotides or with restriction enzyme digests of each clone. Those clones with similar call numbers are placed close together in the ordered library. We address the design question of how many clones and probes to use to carry out in vitro reconstruction of an organism's chromosomes. This physical mapping problem is placed in the context of coverage problems in geometrical probability. Various statistics are developed to summarize how an ordered library covers a chromosome, the extent of clone overlap, and the similarity between clone call numbers. Several tests for whether clones overlap are given, together with their power properties. A simulation study is used to determine how robust some of the tests for clone overlap are to model violations. Tables are presented for researchers to choose the number of clones and probes on the basis of both power and technical considerations surrounding the hybridization experiments.

The DNA of an organism can be digested into smaller fragments, stored individually as clones in phage, for example, to create a clone library, and retrieved later, when needed. The original ordering of fragments is lost in the process of creating the library. Hence, it is important to be able to place clones in order according to their position along chromosome(s), and this process is referred to as "in vitro reconstruction" or "contig mapping" of an organismal genome. Clones in the phage library can be assigned binary call numbers by scoring each clone for hybridization (0 or 1) with a battery of short manufactured DNA sequences called synthetic oligonucleotides or with restriction enzyme digests of each clone. Those clones with similar call numbers are placed close together in the ordered library. We address the design question of how many clones and probes to use to carry out in vitro reconstruction of an organism's chromosomes. This physical mapping problem is placed in the context of coverage problems in geometrical probability. Various statistics are developed to summarize how an ordered library covers a chromosome, the extent of clone overlap, and the similarity between clone call numbers. Several tests for whether clones overlap are given, together with their power properties. A simulation study is used to determine how robust some of the tests for clone overlap are to model violations. Tables are presented for researchers to choose the number of clones and probes on the basis of both power and technical considerations surrounding the hybridization experiments.