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...

In 2009, Oracle replaced the long-serving sorting algorithm in its Java 7 runtime library by a new dual pivot Quicksort variant due to Yaroslavskiy. The decision was based on the strikingly good performance of Yaroslavskiy’s implementation in running time experiments. At that time, no precise investigations of the algorithm were available to explain its superior performance — on the contrary: P...

I discuss the new dual-pivot Quicksort that is nowadays used to sort arrays of primitive types in Java. I sketch theoretical analyses of this algorithm that offer a possible, and in my opinion plausible, explanation why (a) dual-pivot Quicksort is faster than the previously used (classic) Quicksort and (b) why this improvement was not already found much earlier.

An industrial grade Quicksort function along with its new algorithm is presented. Compared to 4 other well known implementations of Quicksort, the new algorithm reduces both the number of comparisons and swaps in most cases while staying close to the best of the 4 in worst cases. We trade space for performance, at the price of n/2 temporary extra spaces in the worst case. Run time tests reveal ...

We consider the standard Quicksort algorithm that sorts n distinct keys with all possible n! orderings of keys being equally likely. Equivalently, we analyze the total path length n in a randomly built binary search tree. Obtaining the limiting distribution of n is still an outstanding open problem. In this paper, we establish an integral equation for the probability density of the number of co...

We develop a series of quicksort algorithms for the Sequent Symmetry shared memory parallel computer. By employing a novel yet simple parallel splitting algorithm and dynamic scheduling we are able to achieve a speedup of 13 with 16 processors over the performance of sequential quicksort on one processor. This work provides experimental evidence that asynchronous algorithms’ more uniform usage ...

Partitioning is a central component of the Quicksort which is an intriguing sorting algorithm, and is a part of C, C++ and Java libraries. Partitioning is a key component of Quicksort, on which the performance of Quicksort ultimately depends. There have been some elegant partitioning algorithms; Profound understanding of prior may be needed if one has to choose among those partitioning algorith...

In this paper we introduce a cost optimal parallel quicksort algorithm. It sorts an array of n elements in O(log n) time using O( n n log ) processors on a CREW PRAM. That is, the total cost is O(n log n), the same as an average sequential quicksort algorithm. The key feature of the proposed algorithm is that it partitions the array concurrently. This removes the performance bottleneck proposed...

Quicksort is the preferred in-place sorting algorithm in many contexts, since its average computing time on uniformly distributed inputs is (N log N) and it is in fact faster than most other sorting algorithms on most inputs. Its drawback is that its worst-case time bound is (N 2). Previous attempts to protect against the worst case by improving the way quicksort chooses pivot elements for part...

In this lecture we consider two related algorithms for sorting that achieve a much better running time than the selection sort from an earlier lecture: mergesort and quicksort. We develop quicksort and its invariants in detail. As usual, contracts and loop invariants will bridge the gap between the abstract idea of the algorithm and its implementation. We will revisit many of the computational ...