  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.
