A new dynamic programming algorithm for the simplified partial digest problem

Abstract

The simplified partial digest problem (SPDP) models an effective and robust method for building physical maps using restriction site analysis. Blazewicz and Kasprzak proved that SPDP is NP-hard. The best-known solution for SPDP is an O(n1.52n/2)-time backtracking algorithm, where n is the number of sites. Blazewicz et al. had an O(n2q)-time dynamic programming algorithm, where q≤n+1 is the number of distinct intersite distances. When q is small, their algorithm solves SPDP efficiently. We give a new dynamic programming algorithm that requires O(qn(n/q+1)q−1) time. This time complexity is O(nq) for any q and is better than O(n1.52n/2) when q≤n/6. For example, for q=n/7, the running time is O(n223n/7). We also give an O(nlgn)-time algorithm for q=2. This result improves the previous upper bound of O(n4) and solves an open problem by Blazewicz and Kasprzak.