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Article Dans Une Revue Theoretical Computer Science Année : 2009

A variant of the tandem duplication - random loss model of genome rearrangement

Résumé

In Soda'06, Chaudhuri, Chen, Mihaescu and Rao study algorithmic properties of the tandem duplication - random loss model of genome rearrangement, well-known in evolutionary biology. In their model, the cost of one step of duplication-loss of width k is $\alpha^k$ for $\alpha =1$ or $\alpha >=2 $. In this paper, we study a variant of this model, where the cost of one step of width $k$ is 1 if $k <= K$ and $\infty$ if $k > K$, for any value of the parameter $K in N$. We first show that permutations obtained after $p$ steps of width $K$ define classes of pattern-avoiding permutations. We also compute the numbers of duplication-loss steps of width $K$ necessary and sufficient to obtain any permutation of $S_n$, in the worst case and on average. In this second part, we may also consider the case $K=K(n)$, a function of the size $n$ of the permutation on which the duplication-loss operations are performed.

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Dates et versions

hal-00206178 , version 1 (16-01-2008)

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Mathilde Bouvel, Dominique Rossin. A variant of the tandem duplication - random loss model of genome rearrangement. Theoretical Computer Science, 2009, 410 (8-10), pp.847-858. ⟨10.1016/j.tcs.2008.11.017⟩. ⟨hal-00206178⟩
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