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
Inversion Medians Outperform Breakpoint Medians in Phylogeny Reconstruction from Gene-Order Data
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
Finding All Common Intervals of k Permutations
CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
INFORMS Journal on Computing
Genome Rearrangement Based on Reversals that Preserve Conserved Intervals
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Using median sets for inferring phylogenetic trees
Bioinformatics
Advances on sorting by reversals
Discrete Applied Mathematics
Perfect Sorting by Reversals Is Not Always Difficult
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Evolution under Reversals: Parsimony and Conservation of Common Intervals
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Computing Common Intervals of $K$ Permutations, with Applications to Modular Decomposition of Graphs
SIAM Journal on Discrete Mathematics
A parallel algorithm for solving the reversal median problem
PPAM'05 Proceedings of the 6th international conference on Parallel Processing and Applied Mathematics
Computing common intervals of K permutations, with applications to modular decomposition of graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
The reversal median problem, common intervals, and mitochondrial gene orders
CompLife'06 Proceedings of the Second international conference on Computational Life Sciences
Conservation of combinatorial structures in evolution scenarios
RCG'04 Proceedings of the 2004 RECOMB international conference on Comparative Genomics
Preserving inversion phylogeny reconstruction
WABI'12 Proceedings of the 12th international conference on Algorithms in Bioinformatics
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Genomic rearrangement operations can be very useful to infer the phylogenetic relationship of gene orders representing species. We study the problem of finding potential ancestral gene orders for the gene orders of given taxa, such that the corresponding rearrangement scenario has a minimal number of reversals, and where each of the reversals has to preserve the common intervals of the given input gene orders. Common intervals identify sets of genes that occur consecutively in all input gene orders. The problem of finding such an ancestral gene order is called the preserving reversal median problem (pRMP). A tree-based data structure for the representation of the common intervals of all input gene orders is used in our exact algorithm TCIP for solving the pRMP. It is known that the minimum number of reversals to transform one gene order into another can be computed in polynomial time, whereas the corresponding problem with the restriction that common intervals should not be destroyed is already NP-hard. It is shown theoretically that TCIP can solve a large class of pRMP instances in polynomial time. Empirically we show the good performance of TCIP on biological and artificial data.