Optimal algorithms for recombination distance problem

Abstract

Recombination of sequences is an important combinatorial optimization problem due to its applications in computational biology. It is related to the alignment with recombination which is an edit distance problem involved recombination, and reconstructing a history of recombination from a set of sequences, etc. Recently, Wu and Gu discussed a distance problem involved recombination consisting of single crossover. [S. Wu and X. Gu (2001). A Greedy algorithm for optimal recombination. Proceeding of COCOON2001, Lecture Notes in Computer Science 2108, pp. 86–90.] 𝒜 and 𝒮 denote two collections of sequences where |𝒮| = 2. The goal is to generate 𝒜 from 𝒮 by a series of recombinations in minimum number of steps. They defined a special class 𝒜 of sequences called ‘tree’, and presented a greedy algorithm which was claimed optimal for finding the recombination distance from 𝒮 to 𝒜. In this paper, we revisit this result. We show that the greedy algorithm is not always optimal, and propose a revised algorithm which can solve the problem optimally. We further propose a new class 𝒜 of sequences called ‘chain’ and provide a polynomial time algorithm for finding the optimal recombination evolutionary history from 𝒮 to 𝒜. †chenting@math.zju.edu.cn