Fig. 9

In a, an example array A with 8 pairs. In b, we show how A, P, and R are updated by decrease-value(e). After \(\textsc {Swap} ({i,j})\) and the decrease of the value of e from 8 to 6, there is no element 6 in R, hence \(6 \rightarrow [5,6)\) is added to R (line 11 of Algorithm 8) and \(R[8].begin \) incremented by 1. Note that if the value of y were 6, then the test at line 10 would have succeeded, hence \(R[6].end \) would have been updated