This paper presents an algorithm for fast sorting of large lists using modern GPUs. The method achieves high speed by efficiently utilizing the parallelism of the GPU throughout the whole algorithm. Initially, GPU-based bucketsort or quicksort splits the list into enough sublists then to be sorted in parallel using merge-sort. The algorithm is of complexity n log n, and for lists of 8M elements...

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 ...

This paper presents and evaluates an alternative sorting component for Hadoop based on the replacement selection algorithm. In comparison with the default quicksort-based implementation, replacement selection generates runs which are in average twice as large. This makes the merge phase more efficient, since the amount of data that can be merged in one pass increases in average by a factor of t...

The main theme of this class is randomized algorithms. We start by comparing these to the deterministic algorithms to which we are so accustomed. In the deterministic model of computation (Turing machines and RAM), an algorithm has fixed behavior on every fixed input. In contrast, in the randomized model of computation, algorithms take additional input consisting of a stream of random bits. The...

Problem 1. Write a Prolog program, consisting only of pure Horn clauses, that orders a list of natural numbers by the quicksort algorithm. Problem 2. Write a Prolog program, consisting only of pure Horn clauses, that computes all permutations of a given list. Problem 3. Write a Prolog program, consisting only of pure Horn clauses, that nds all normal magic squares of order 3. Please consult Wik...

Hoare’s FIND algorithm can be used to select the jth element out of a file of n elements. It bears a remarkable similarity to Quicksort; in each pass of the algorithm, a pivot element is used to split the file into two subfiles, and recursively the algorithm proceeds with the subfile that contains the sought element. As in Quicksort, different strategies for selecting the pivot are reasonable. ...

The weak limit of the normalized number of comparisons needed by the Quicksort algorithm to sort n randomly permuted items is known to be determined implicitly by a distributional fixed-point equation. We give an algorithm for perfect random variate generation from this distribution.

Quicksort [5] remains one of the most studied algorithms in computer science. It is important not only as a practical sorting method, but also as a splendid teaching aid for introducing recursion and systematic algorithm development. The algorithm has been studied extensively; so, it is natural to assume that everything that needs to be said about it has already been said. Yet, in attempting to...

Smoothed analysis is a framework for analyzing the complexity of an algorithm, acting as a bridge between average and worst-case behaviour. For example, Quicksort and the Simplex algorithm are widely used in practical applications, despite their heavy worst-case complexity. Smoothed complexity aims to better characterize such algorithms. Existing theoretical bounds for the smoothed complexity o...

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...