  Multi-Pivot Quicksort refers to variants of classical quicksort where in the
partitioning step $k$ pivots are used to split the input into $k + 1$ segments.
For many years, multi-pivot quicksort was regarded as impractical, but in 2009
a 2-pivot approach by Yaroslavskiy, Bentley, and Bloch was chosen as the
standard sorting algorithm in Sun's Java 7. In 2014 at ALENEX, Kushagra et al.
introduced an even faster algorithm that uses three pivots. This paper studies
what possible advantages multi-pivot quicksort might offer in general. The
contributions are as follows: Natural comparison-optimal algorithms for
multi-pivot quicksort are devised and analyzed. The analysis shows that the
benefits of using multiple pivots with respect to the average comparison count
are marginal and these strategies are inferior to simpler strategies such as
the well known median-of-$k$ approach. A substantial part of the partitioning
cost is caused by rearranging elements. A rigorous analysis of an algorithm for
rearranging elements in the partitioning step is carried out, observing mainly
how often array cells are accessed during partitioning. The algorithm behaves
best if 3 to 5 pivots are used. Experiments show that this translates into good
cache behavior and is closest to predicting observed running times of
multi-pivot quicksort algorithms. Finally, it is studied how choosing pivots
from a sample affects sorting cost. The study is theoretical in the sense that
although the findings motivate design recommendations for multipivot quicksort
algorithms that lead to running time improvements over known algorithms in an
experimental setting, these improvements are small.
