Design of shortest double-stranded DNA sequences covering all k-mers with applications to protein-binding microarrays and synthetic enhancers

doi:10.1093/bioinformatics/btt230 Bioinformatics (2013) 29(13), i71–i79

In the above paper, there were several mistakes due to copyediting error. In Theorem 1 ‘if’ should be replaced by ‘iff’ and should read as follows: For odd k, an RC complete sequence s achieves the lower bound (Proposition 1) iff there exist two edge-disjoint paths with no repeating edges, corresponding to s and RC(s), that together cover all edges of the de Bruijn graph of order k − 1.

In Algorithm 1 ‘although’ should be replaced by ‘while’, and should read as follows:

1. Initially all edges are unmarked, $\mathcal{F}=\mathcal{R}=\varnothing$,

 and $A=\left\{u\right\}$, an arbitrary vertex.

2. While $A\ne \varnothing$ do

3.  $F=R=\varnothing$.

4.   Pick any starting vertex $v=[x_1,\dots ,x_{k-1}]$ from A.

5.   While there exists an unmarked edge $e=(x_1,\dots ,x_k)$

   outgoing from v do

6.    Append e to F. Prepend RC(e) to R.

7.    Mark e and RC(e).

8.    Set $v=[x_2,\dots ,x_k]$; $A=A\cup \left\{v\right\}$.

9.   Remove v from A.

10.   If $F\ne \varnothing$, add F to $\mathcal{F}$; add R to $\mathcal{R}$;

11. Merge the cycles in $\mathcal{F}$ to obtain a single forward path.

  Do the same for $\mathcal{R}$.