SUMMARY We develop a balanced, parallel quicksort algorithm for a hypercube and compare it with a similar algorithm for a binary tree machine. The performance of the hypercube algorithm is measured on a Computing Surface.

In this lecture we use Azuma’s inequality to analyze the randomized Quicksort algorithm. Quicksort takes as input a set S of numbers, which can be assumed to be distinct without loss of generality, and sorts the set S as follows: it picks a pivot x ∈ S uniformly at random, then it partitions the set S as Sx = {y ∈ S | y > x}, and recursively sorts Sx . The fo...

Speed: Randomized algorithms are usually fast, sometimes much faster than any deterministic algorithm for the same problem. Even if the asymptotic running time is the same as the deterministic one it can be faster in practice. For example QuickSort, though has worse-case running time worse than that of MergeSort or Heapsort, it is the fastest algorithm in practice. The disadvantage of some rand...

This paper describes a new algorithm of arrangement in parallel, based on Odd-Even Mergesort, called division and concurrent mixes. The main idea of the algorithm is to achieve that each processor uses a sequential algorithm for ordering a part of the vector, and after that, for making the processors work in pairs in order to mix two of these sections ordered in a greater one, also ordered; aft...

In this write-up, we extend quicksort to the task of fuzzy sorting of intervals. In many situations the precise value of a quantity is uncertain (e.g., any physical measurement is subject to noise). For such situations we may represent a measurement i as a closed interval [ai, bi], where ai ≤ bi. A fuzzysort is defined as a permutation 〈i1, i2, . . . , in〉 of the intervals such that there exist...

Based on the current fiber optic technology, a new computational model, called a linear array with a reconfigurable pipelined bus system (LARPBS), is proposed in this paper. A parallel quicksort algorithm is implemented on the model, and its time complexity is analyzed. For a set of N numbers, the quicksort algorithm reported in this paper runs in O(log, N) average time on a linear array with a...

The earlier SCM computer did not contain recursive function, so Trybulec and Nakamura proved the correctness of the Euclid’s algorithm only by way of an iterative program. However, the recursive method is a very important programming method, furthermore, for some algorithms, for example Quicksort, only by employing a recursive method (note push-down stack is essentially also a recursive method)...