Improved Approximation Algorithms for Reconstructing the History of Tandem Repeats

Some genetic diseases in human beings are dominated by short sequences repeated consecutively called tandem repeats. Once a region containing tandem repeats is found, it is of great interest to study the history of creating the repeats. The computational problem of reconstructing the duplication history of tandem repeats has been studied extensively in the literature. Almost all previous studies focused on the simplest case where the size of each duplication block is 1. Only recently we succeeded in giving the first polynomial-time approximation algorithm with a guaranteed ratio for a more general case where the size of each duplication block is at most 2; the algorithm achieves a ratio of 6 and runs in O(n
¹¹
) time. In this paper, we present two new polynomial-time approximation algorithms for this more general case. One of them achieves a ratio of 5 and runs in O(n
⁹
) time, while the other achieves a ratio of 2.5+ isin for any constant isin > 0 but runs slower.