Tandem halving problems by DCJ

Abstract

We address the problem of reconstructing a non-duplicated ancestor to a partially duplicated genome in a model where duplicated content is caused by several tandem duplications throughout its evolution and the only allowed rearrangement operations are DCJ. As a starting point, we consider a variant of the Genome Halving Problem, aiming at reconstructing a tandem duplicated genome instead of the traditional perfectly duplicated genome. We provide a distance in O(n) time and a scenario in O(n 2) time. In an attempt to enhance our model, we consider several problems related to multiple tandem reconstruction. Unfortunately we show that although the problem of reconstructing a single tandem can be solved polynomially, it is already NP-hard for 2 tandems. © 2012 Springer-Verlag.