Fig. 2

A Example of text overlap. The substring \(R[x-1\ldots y]=\texttt {atgcc}\) encodes two k-mers, \(R[x-1\ldots y-1] = \texttt {atgc}\) and \(R[x\ldots y]=\texttt {tgcc}\). Let us assume the canonical \(K^{c}_{pr} \in \{K_{pr}, \hat{K}_{pr}\}\) matches the DNA reverse complement of \(R[x-1\ldots y-1]\), i.e., \(\texttt {gcat}\). On the other hand, let us assume \(R[x\ldots y]=K^{c}\) matches the canonical of \(\{K,\hat{K}\}\). Thus, the relative DNA orientation of \(R[x-1\ldots y-1] \oplus R[x\ldots y]\) with respect to \(K^{c}\) is \(\hat{K}^{c}_{pr} \oplus K^{c}\). This means that \(K^{c}[k-1] = \pi (K^{c}_{pr}[1])=\texttt {c}\) is the symbol we obtain from the link H[b].r in \(K^{c}\)’s bucket H[b]. The grey arrow from H to the grey rectangle depicts this situation. B Text overlaps for \(K^{c}_{pr}\) and \(K^{c}\) relative to \(K^{c}\)’s DNA orientation. The x marks the symbol in \(K^{c}\) we obtain by following H[b].r