Optimal Sampling Strategies in Quicksort and Quickselect

Partitioning schemes for quicksort and quickselect

We introduce several modifications of the partitioning schemes used in Hoare’s quicksort and quickselect algorithms, including ternary schemes which identify keys less or greater than the pivot. We give estimates for the numbers of swaps made by each scheme. Our computational experiments indicate that ternary schemes allow quickselect to identify all keys equal to the selected key at little add...

Chapter 13 Introduction to Randomized Algorithms: QuickSort and QuickSelect

Chunksort: A Generalized Partial Sorting Algorithm

We introduce here the problem of generalized partial sorting and chunksort, an algorithm closely related to quicksort and quickselect that solves this problem in an elegant and efficient way. In generalized partial sorting we are given an array of n elements and p intervals I1 = [`1,u1], I2 = [`2,u2], . . . , Ip = [`p,up], which define p blocks in the array and p+1 gaps between the blocks. The ...

The Number of Symbol Comparisons in QuickSort and QuickSelect

We revisit the classical QuickSort and QuickSelect algorithms, under a complexity model that fully takes into account the elementary comparisons between symbols composing the records to be processed. Our probabilistic models belong to a broad category of information sources that encompasses memoryless (i.e., independent-symbols) and Markov sources, as well as many unbounded-correlation sources....

Moves and displacements of particular elements in Quicksort

In this research note we investigate the number of moves and the displacement of particular elements during the execution of the well-known quicksort algorithm. This type of analysis is useful if the costs of data moves were dependent on the source and target locations, and possibly the moved element itself. From the mathematical point of view, the analysis of these quantities turns out to be r...