Showing papers on "Comparison sort published in 1989"
TL;DR: The main result is an optimal randomized parallel algorithm for INTEGER_SORT, the first known that is optimal: the product of its time and processor bounds is upper bounded by a linear function of the input size.
Abstract: This paper assumes a parallel RAM (random access machine) model which allows both concurrent reads and concurrent writes of a global memory.The main result is an optimal randomized parallel algorithm for INTEGER_SORT (i.e., for sorting n integers in the range $[1,n]$). This algorithm costs only logarithmic time and is the first known that is optimal: the product of its time and processor bounds is upper bounded by a linear function of the input size. Also given is a deterministic sublogarithmic time algorithm for prefix sum. In addition this paper presents a sublogarithmic time algorithm for obtaining a random permutation of n elements in parallel. And finally, sublogarithmic time algorithms for GENERAL_SORT and INTEGER_SORT are presented. Our sub-logarithmic GENERAL_SORT algorithm is also optimal.
175 citations
TL;DR: Two measures of presortedness, Dist(X) and logDist(X), are presented and an exact characterization of the local insertion sort algorithm of Mannila is achieved.
Abstract: Two measures of presortedness, Dist(X) and logDist(X), are presented. The measures are motivated by a geometric interpretation of the input sequence X. Using these measures, an exact characterization of the local insertion sort algorithm of Mannila is achieved. Variants of local insertion sort, using many fingers (i.e., pointers into a finger search tree) instead of only one, are suggested. The number can either be fixed beforehand or dynamic, i.e., vary during the sorting process. Different strategies for moving the fingers yield different algorithms. Some general conditions which all strategies should satisfy are stated, and two such strategies are given. Furthermore, a method for designing dynamic algorithms that allocate an optimal number of fingers is provided. For any specific strategy satisfying our conditions, this method yields an optimal algorithm.
10 citations
TL;DR: The time complexity of Thompson and Kung's s/sup 2/-way merge sort is analyzed and shown to be asymptotically optimal with respect to the recently improved lower bound on sorting on a mesh-connected n*n array.
Abstract: The time complexity of Thompson and Kung's (1977) s/sup 2/-way merge sort is analyzed and shown to be asymptotically optimal with respect to the recently improved lower bound on sorting on a mesh-connected n*n array. New lower bounds for systolic sorting are derived. A systolic version of s/sup 2/-way merge sort is systematically constructed and shown to be asymptotically optimal as well. >
5 citations
Patent•
13 Nov 1989TL;DR: An error collection method for a sorter system having n pipelined sort elements of the same type and n local memories Mi (i=1-n) each connected to the corresponding sort element and having a memory capacity of at least 2 i-1 record length is presented in this article.
Abstract: An error collection method for a sorter system having n pipelined sort elements Pi (i=1-n) of the same type and n local memories Mi (i=1-n) each connected to the corresponding sort element and having a memory capacity of at least 2 i-1 record length, which includes the steps of sorting in said sort elements when one of the sort elements detects a fault; reporting contents of an error to the upper structure; analyzing the error; and restarting sorting.
4 citations
IBM1
TL;DR: A table-lookup technique for sorting is developed which develops an approximation to the sort through a single access to an associative memory and is most effective for special data classes.
3 citations
22 Mar 1989
TL;DR: A parallel sorting algorithm is introduced which is based on the odd-even transposition (or exchange) sorting scheme and it is shown that this algorithm can outperform comparable parallel exchange sort algorithms.
Abstract: A parallel sorting algorithm is introduced which is based on the odd-even transposition (or exchange) sorting scheme. Compared to the parallel sorters of its class, the proposed algorithm requires about the same time complexity but reduces the number of processing elements in half. Using the VLSI measure of area*time/sup 2/, it is shown that this algorithm can outperform comparable parallel exchange sort algorithms. Due to its simple cell design and regular interconnections, the proposed sorter is highly suitable for VLSI implementation. >
3 citations