A fast algorithm for the partial digest problem

A fundamental problem in computational biology is the restriction site mapping. When a particular restriction enzyme is added to a DNA, the DNA strand is cut at particular restriction sites. The goal of the restriction site mapping is to determine the location of every site for a given enzyme. Using gel electrophoresis, one can find the distance between each pair of restriction sites. In the partial digest problem (PDP), we are given these distances arising from digestion experiments by using only one enzyme, and we are asked to compute the locations of all restriction sites. Several approaches, including pseudo-polynomial time algorithm and backtracking algorithm have been proposed to tackle this problem. In this paper we propose a new model for this problem. Based on this model, we present a new branch and bound algorithm for partial digest problem. In comparison with the backtracking algorithm presented by Skiena, the new algorithm has very small search tree and so it is very efficient. The efficiency and advantages of this algorithm are also demonstrated by executing it on different types of instances. There exist some instances of PDP , where the Skiena’s algorithm requires exponential running time to solve them. The efficiency of our algorithm is also presented for these kind of problem instances.