Conserved synteny as a measure of genomic distance
Discrete Applied Mathematics - Special volume on computational molecular biology
On the complexity and approximation of syntenic distance
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
Sorting permutations by tanspositions
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
Open Combinatorial Problems in computational Molecular Biology
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Genome rearrangements and sorting by reversals
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Structural Properties and Tractability Results for Linear Synteny
COM '00 Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching
Edit Distance with Move Operations
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
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This paper examines some of the rich structure of the syntenic distance model of evolutionary distance, introduced by Ferretti, Nadeau, and Sankoff. The syntenic distance between two genomes is the minimum number of fissions, fusions, and translocations required to transform one into the other, ignoring gene order within chromosomes. We prove that the previously unanalyzed algorithm given by Ferretti et al is a 2-approximation and no better, and that, further, it always outperforms the algorithm presented by DasGupta, Jiang, Kannan, Li, and Sweedyk. We also prove the same results for an improved version of the Ferretti et al algorithm. We then prove a number of properties which give insight into the structure of optimal move sequences. We give instances in which any move sequence working solely within connected components is nearly twice optimal, and a general lower bound based on the spread of genes from each chromosome. We then prove a monotonicity property for the syntenic distance, and bound the difficulty of the hardest instance of any given size. We briefly discuss the results of implementing these algorithms and testing them on real synteny data.