The gene order on a chromosome is a necessary data for most comparative genomics studies, but in many cases only partial orders can be obtained by current genetic mapping techniques. The Minimum Breakpoint Linearization Problem aims at constructing a total order from this partial knowledge, such that the breakpoint distance to a reference genome is minimized. In this paper, we first expose a flaw in two algorithms formerly known for this problem [6], [4]. We then present a new modeling for this problem, and use it to design three approximation algorithms, with ratios resp. , and , where is the optimal breakpoint distance we look for, is upper bounded by the number of pairs of genes for which the partial order is in contradiction with the reference genome, and is the number of genetic maps used to create the input partial order.
A preliminary version of this paper appeared in the proceedings of the 7th Annual Conference on Theory and Applications of Models of Computation, TAMC 2010 [3].