Formulations and hardness of multiple sorting by reversals
RECOMB '99 Proceedings of the third annual international conference on Computational molecular biology
Rank aggregation methods for the Web
Proceedings of the 10th international conference on World Wide Web
Approximating Minimum Feedback Sets and Multi-Cuts in Directed Graphs
Proceedings of the 4th International IPCO Conference on Integer Programming and Combinatorial Optimization
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Phylogenetic Reconstruction from Arbitrary Gene-Order Data
BIBE '04 Proceedings of the 4th IEEE Symposium on Bioinformatics and Bioengineering
Aggregating inconsistent information: ranking and clustering
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Genomic distances under deletions and insertions
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Genome rearrangement in mitochondria and its computational biology
RCG'04 Proceedings of the 2004 RECOMB international conference on Comparative Genomics
Aggregating inconsistent information: Ranking and clustering
Journal of the ACM (JACM)
An Algorithm for Inferring Mitogenome Rearrangements in a Phylogenetic Tree
RECOMB-CG '08 Proceedings of the international workshop on Comparative Genomics
A variant of the tandem duplication — random loss model of genome rearrangement
Theoretical Computer Science
Finding All Sorting Tandem Duplication Random Loss Operations
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Posets and permutations in the duplication-loss model: Minimal permutations with d descents
Theoretical Computer Science
Whole mirror duplication-random loss model and pattern avoiding permutations
Information Processing Letters
Minimal permutations with d descents
European Journal of Combinatorics
Efficient algorithms for analyzing segmental duplications, deletions, and inversions in genomes
WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
Finding all sorting tandem duplication random loss operations
Journal of Discrete Algorithms
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We initiate the algorithmic study of a new model of genome rearrangement, the tandem duplication-random loss model, in which a genome evolves via successive rounds of tandem duplication of a contiguous segment of genes, followed by the loss of one copy of each of the duplicated genes. This model is well-known in the evolutionary biology literature, where it has been used to explain many of the known rearrangements in vertebrate mitochondrial genomes. Based on the model, we formalize a notion of distance between two genomes and show how to compute it efficiently for two interesting regions of the parameter space. We then consider median problems (i.e. finding the point which minimizes the sum of distances to a given set of points under some distance function) in the context of maximum parsimony phylogenetic reconstruction for these two special cases. Surprisingly, one of them turns out to correspond to the well-known rank aggregation problem, while the other corresponds to the biologically interesting case of whole genome duplication and loss, and we give an O(log log n) additive approximation algorithm for the latter.