For partitioned data, if the list of pivots is stored (for example, in a sorted list of the indices), then subsequent selections only need to select in the interval between two pivots (the nearest pivots below and above). The biggest gain is from the top-level pivots, which eliminate costly large partitions: a single pivot near the middle of the data cuts the time for future selections in half. The pivot list will grow over subsequent selections, as the data becomes more sorted, and can even be passed to a partition-based sort as the basis of a full sort.