Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Efficient algorithms for multichromosomal genome rearrangements
Journal of Computer and System Sciences - Computational biology 2002
Finding an Optimal Inversion Median: Experimental Results
WABI '01 Proceedings of the First International Workshop on Algorithms in Bioinformatics
Transforming men into mice (polynomial algorithm for genomic distance problem)
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
INFORMS Journal on Computing
Multichromosomal Genome Median and Halving Problems
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
Decompositions of Multiple Breakpoint Graphs and Rapid Exact Solutions to the Median Problem
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
A Fast and Exact Algorithm for the Median of Three Problem--A Graph Decomposition Approach
RECOMB-CG '08 Proceedings of the international workshop on Comparative Genomics
Sorting Signed Permutations by Inversions in O(nlogn) Time
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
Reactive stochastic local search algorithms for the genomic median problem
EvoCOP'08 Proceedings of the 8th European conference on Evolutionary computation in combinatorial optimization
On exploring genome rearrangement phylogenetic patterns
RECOMB-CG'10 Proceedings of the 2010 international conference on Comparative genomics
The transposition median problem is NP-complete
Theoretical Computer Science
GASTS: parsimony scoring under rearrangements
WABI'11 Proceedings of the 11th international conference on Algorithms in bioinformatics
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Given a set of genomes $\mathcal{G}$ and a distance measure d , the genome rearrangement median problem asks for another genome q that minimizes $\sum_{g\in \mathcal{G}} d(q,g)$. This problem lies at the heart of phylogenetic reconstruction from rearrangement data, where solutions to the median problems are iteratively used to update genome assignments to internal nodes for a given tree. The median problem for reversal distance and DCJ distance is known to be NP-hard, regardless of whether genomes contain circular chromosomes or linear chromosomes and of whether extra circular chromosomes is allowed in the median genomes. In this paper, we study the relaxed DCJ median problem on linear multichromosomal genomes where the median genomes may contain extra circular chromosomes; extend our prior results on circular genomes--which allowed us to compute exact medians for genomes of up to 1,000 genes within a few minutes. First we model the DCJ median problem on linear multichromosomal genomes by a capped multiple breakpoint graph , a model that avoids another computationally difficult problem--a multi-way capping problem for linear genomes, then establish its corresponding decomposition theory, and finally show its results on genomes with up to several thousand genes.