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Approximate counting of inversions in a data stream
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Gossip is synteny: incomplete gossip and the syntenic distance between genomes
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Approximating the Expected Number of Inversions Given the Number of Breakpoints
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Packing Cycles and Cuts in Undirected Graphs
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
(1+epsilon)-Approximation of Sorting by Reversals and Transpositions
WABI '01 Proceedings of the First International Workshop on Algorithms in Bioinformatics
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Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
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Information Processing Letters
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Information and Computation
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CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
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Applied Intelligence
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SIAM Journal on Computing
Approximation algorithms for grooming in optical network design
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SIAM Journal on Discrete Mathematics
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WABI'06 Proceedings of the 6th international conference on Algorithms in Bioinformatics
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ESA'05 Proceedings of the 13th annual European conference on Algorithms
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WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
Reversal distance for strings with duplicates: linear time approximation using hitting set
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Sorting by weighted reversals, transpositions, and inverted transpositions
RECOMB'06 Proceedings of the 10th annual international conference on Research in Computational Molecular Biology
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Proceedings of the 27th Annual ACM Symposium on Applied Computing
Heuristics for the Sorting by Length-Weighted Inversion Problem
Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics
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We analyze the strong relationship among three combinatorial problems, namely, the problem of sorting a permutation by the minimum number of reversals (MIN-SBR), the problem of finding the maximum number of edge-disjoint alternating cycles in a breakpoint graph associated with a given permutation (MAX-ACD), and the problem of partitioning the edge set of an Eulerian graph into the maximum number of cycles (MAX-ECD). We first illustrate a nice characterization of breakpoint graphs, which leads to a linear-time algorithm for their recognition. This characterization is used to prove that MAX-ECD and MAX-ACD are equivalent, showing the latter to be NP-hard. We then describe a transformation from MAX-ACD to MIN-SBR, which is therefore shown to be NP-hard as well, answering an outstanding question which has been open for some years. Finally, we derive the worst-case performance of a well-known lower bound for MIN-SBR, obtained by solving MAX-ACD, discussing its implications on approximation algorithms for MIN-SBR.