Abstract
In this paper, we describe an algorithm to stably sort an array ofn elements using only a linear number of data movements and constant extra space, albeit in quadratic time. It was not known previously whether such an algorithm existed. When the input contains only a constant number of distinct values, we present a sequence ofin situ stable sorting algorithms makingO(n lg(k+1) n+kn) comparisons (lg(K) means lg iteratedk times and lg* the number of times the logarithm must be taken to give a result ≤ 0) andO(kn) data movements for any fixed valuek, culminating in one that makesO(n lg*n) comparisons and data movements. Stable versions of quicksort follow from these algorithms.
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Additional information
Research supported by Natural Sciences and Engineering Research Council of Canada grant No.A-8237 and the Information Technology Research Centre of Ontario.
Supported in part by a Research Initiation Grant from the Virginia Engineering Foundation.