Fast Algorithms for the Simplified Partial Digest Problem

The simplified partial digest problem (SPDP) models an effective and robust method for the building of a physical map using restriction site analysis. The best known algorithm requires O(n2) time, using O(n2) working space. The high complexities in time and space impede its application to genomes of a large number of sites. This article gives two new algorithms. The first improves the time by a factor of O(n) and significantly reduces the space to O(n²). The second improves both the time and space to O(n^1.52). Extensive experiments are conducted on real genomes. For instances that can be solved by the best known algorithm, the new algorithms achieve a speedup of up to 4000 times; in addition, due to the reduction in space, the new algorithms can solve many more instances. Experiments also reveal the following advantage of the SPDP method: almost every instance has at most four feasible solutions and for an instance that does not contain any pair of symmetric restriction sites, in all observed examples, the solution is unique.