Elsevier

Theoretical Computer Science

Volume 494, 8 July 2013, Pages 122-133
Theoretical Computer Science

Revisiting the Minimum Breakpoint Linearization Problem

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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  [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+4m4, 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.

Keywords

Comparative genomics
Breakpoint distance
Partially ordered genome
Approximation algorithms

Cited by (0)

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].