Three new computer algorithms are described which rapidly order the restriction fragments of a plasmid DNA which has been cleaved with two restriction endonucleases in single and double digestions. Two of the algorithms are contained within a single computer program (called MPCIRC). The Rule-Oriented algorithm, constructs all logical circular map solutions within sixty seconds (14 double-digestion fragments) when used in conjunction with the Permutation method. The program is written in Apple Pascal and runs on an Apple II Plus Microcomputer with 64K of memory. A third algorithm is described which rapidly maps double digests and uses the above two algorithms as adducts. Modifications of the algorithms for linear mapping are also presented.