A standard technique for mapping a chromosome is to randomly select pieces, to use restriction enzymes to cut these pieces into fragments, and then to use the fragments for estimating the probability of overlap of these pieces. The authors describe a computational approach which has been used in the mapping of human chromosome 16 at Los Alamos National Laboratory. In particular, they describe 6-way and clustered implementations of an IBM Clustered Fortran program for detection of fragment overlap, with specific attention paid to problem partitioning, task structure, synchronization, and other factors which allow this type of code to perform well on a cluster of shared-memory multiprocessors. Measurements for one, six, and twelve processors for reduced problem sizes are included.>