Mikhail Karasikov; Harun Mustafa; Gunnar Rätsch; André Kahles

Lossless indexing with counting de Bruijn graphs

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Figure 3.

Extraction of k-mer coordinates from sequence ACTAGCTAGCTAG for k = 3 (panel A) and subsequent compression with a diff-transform (panel B), where the coordinates at a node's successor are expected to be the same but incremented by +1, as these nodes are likely to be consecutive in the input sequence(s). The symmetric set difference $\text{[math]}$ is used as a diff-operation. Thus, for example, $\text{[math]}$ . The inverse transform is performed losslessly by $\text{[math]}$ , which follows from the following property: $\text{[math]}$ .