The Reconstruction of Doubled Genomes
SIAM Journal on Computing
Combinatorics of Permutations
Sorting by Transpositions Based on the First Increasing Substring Concept
BIBE '04 Proceedings of the 4th IEEE Symposium on Bioinformatics and Bioengineering
On the tandem duplication-random loss model of genome rearrangement
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
New Bounds and Tractable Instances for the Transposition Distance
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Perfect Sorting by Reversals Is Not Always Difficult
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A new tight upper bound on the transposition distance
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
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
Finding all sorting tandem duplication random loss operations
Journal of Discrete Algorithms
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In [K. Chaudhuri, K. Chen, R. Mihaescu, S. Rao, On the tandemduplication-random loss model of genome rearrangement, in: SODA,2006, pp. 564-570], Chaudhuri, Chen, Mihaescu and Rao studyalgorithmic properties of the tandem duplication - randomloss model of genome rearrangement, well-known in evolutionarybiology. In their model, the cost of one step of duplication-lossof width k is αk forα=1 or α≥2. In this paper, we study avariant of this model, where the cost of one step of width kis 1 if k≤K and ∞ if kK,for any value of the parameterKεℕ∪{∞}. We first show thatpermutations obtained after p steps of width K defineclasses of pattern-avoiding permutations. We also compute thenumbers of duplication-loss steps of width K necessary andsufficient to obtain any permutation of Sn, inthe worst case and on average. In this second part, we may alsoconsider the case K=K(n), a function of thesize n of the permutation on which the duplication-lossoperations are performed.