A greedy algorithm for optimal recombination

Abstract

Let Σ be an alphabet and Σn denote the collection of all sequences of length n over Σ. For any s1 = a1a2 ・ ・ ・ ajaj+1 ・ ・ ・ an, s2 = b1b2 ・ ・ ・ bj bj+1 ・ ・ ・ bn ∈ Σn, a recombination of s1 and s2 at position j is defined as an operation that crosses s1 and s2 at position j and generates t1 = a1a2 ・ ・ ・ ajbj+1 ・ ・ ・ bn and t2 = b1b2 ・ ・ ・ bjaj+1 ・ ・ ・ an. Denote A and S two collections of sequences. In this paper, we discuss generating A from S by a series of recombinations in minimum number of steps. We present a greedy algorithm for finding the optimal recombination evolutionary history from S to any tree A of sequences when |S| = 2.