Fig. 1

An example collection \(\mathcal {S}\) of 4 weighted sequences (for \(k=31\)) drawn from the genome of E. coli (Sakai strain). With alternating colors we render the change of weight in the runs. There are 111 \(k\)-mers in the example but just 6 runs in the weights: \(RLW = \langle 5,14 \rangle \langle 4,18 \rangle \langle 2,8 \rangle \langle 1,31 \rangle \langle 4,33 \rangle \langle 13,7 \rangle . \) Note that a run can cross the boundary between two (or more) sequences, as it happens for the run \(\langle 4,18 \rangle \) which covers completely the third but also the part of the second sequence