Approximating Minimum Feedback Sets and Multi-Cuts in Directed Graphs
Proceedings of the 4th International IPCO Conference on Integer Programming and Combinatorial Optimization
Hardness of Approximating Problems on Cubic Graphs
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
Reversal distance for partially ordered genomes
Bioinformatics
An Approximation Algorithm for the Minimum Breakpoint Linearization Problem
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Genome rearrangements with partially ordered chromosomes
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Revisiting the minimum breakpoint linearization problem
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
| Hi-index | 5.23 |
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(log^2(|X|)) and m^2+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.