Constructing the Minimum Founder Set from a Set of Recombinant Sequences

Genetic recombination plays an important role in shaping the within-species genetic variations. It has been generally accepted that current-day population evolved from a small number of specific sequences called founders, and the genomic sequences (called recombinants) of individuals within the population are composed of segments from the founders due to recombination. A related computational problem is the so-called Minimum Founder Set problem: construct the minimum founder set from a set of given recombinant sequences so that the minimum fragment length is not less than the given fragment length bound. Ukkonen presented a segmentation based dynamic programming (SDYN) algorithm to solve it. However, the number of reconstructed founders obtained by the SDYN algorithm is restricted by the given fragment length bound in a certain situation. In this paper, a practical constructive heuristic algorithm HMFS is proposed for solving the problem. The HMFS algorithm partitions the sites of founders into three parts and reconstructs them respectively. Experimental results show that the HMFS algorithm can reconstruct a founder set very quickly, and the solutions obtained by the HMFS algorithm are close to or better than those obtained by the SDYN algorithm. In addition, the HMFS algorithm runs much faster than the SDYN algorithm, it is still efficient for solving large size problems.