Revisiting the Minimum Breakpoint Linearization Problem

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. O(log(k)loglog(k)), O(log2(|X|)) and m2+4m−4, where k is the optimal breakpoint distance we look for, |X| is upper bounded by the number of pairs of genes for which the partial order is in contradiction with the reference genome, and m is the number of genetic maps used to create the input partial order.