Analysis of the Multi-Pivot Quicksort Process

Dual pivot Quicksort

In this paper, we analyse the dual pivot Quicksort, a variant of the standard Quicksort algorithm, in which two pivots are used for the partitioning of the array. We are solving recurrences of the expected number of key comparisons and exchanges performed by the algorithm, obtaining the exact and asymptotic total average values contributing to its time complexity. Further, we compute the averag...

Pivot Sampling in Dual-Pivot Quicksort

The new dual-pivot Quicksort by Vladimir Yaroslavskiy — used in Oracle’s Java runtime library since version 7 — features intriguing asymmetries in its behavior. They were shown to cause a basic variant of this algorithm to use less comparisons than classic single-pivot Quicksort implementations. In this paper, we extend the analysis to the case where the two pivots are chosen as fixed order sta...

Probabilistic Analysis of the Dual-Pivot Quicksort "Count"

Recently, Aumüller and Dietzfelbinger proposed a version of a dual-pivot quicksort, called “Count”, which is optimal among dual-pivot versions with respect to the average number of key comparisons required. In this note we provide further probabilistic analysis of “Count”. We derive an exact formula for the average number of swaps needed by “Count” as well as an asymptotic formula for the varia...

On the Analysis of Two Fundamental Randomized Algorithms - Multi-Pivot Quicksort and Efficient Hash Functions

Average Case Analysis of Java 7's Dual Pivot Quicksort

Recently, a new Quicksort variant due to Yaroslavskiy was chosen as standard sorting method for Oracle’s Java 7 runtime library. The decision for the change was based on empirical studies showing that on average, the new algorithm is faster than the formerly used classic Quicksort. Surprisingly, the improvement was achieved by using a dual pivot approach, an idea that was considered not promisi...