Revisiting the Minimum Breakpoint Linearization Problem

Abstract

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 [4,2]. 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 m 2 + 4m − 4, where k is the optimal breakpoint distance we look for, |X| is upper bounded by the number of pair 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.KeywordsApproximation AlgorithmPartial OrderReference GenomeDirected Acyclic GraphTotal OrderThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.