Affiliation:
1. MADALGO, University of Aarhus, Århus N, Denmark
2. University of Southern Denmark, Odense M, Denmark
3. J. W. Goethe University, Frankfurt/Main, Germany
Abstract
Quicksort was first introduced in 1961 by Hoare. Many variants have been developed, the best of which are among the fastest generic-sorting algorithms available, as testified by the choice of Quicksort as the default sorting algorithm in most programming libraries. Some sorting algorithms are adaptive, i.e., they have a complexity analysis that is better for inputs, which are nearly sorted, according to some specified measure of presortedness. Quicksort is not among these, as it uses Ω(
n
log
n
) comparisons even for sorted inputs. However, in this paper, we demonstrate empirically that the actual running time of Quicksort
is
adaptive with respect to the presortedness measure Inv. Differences close to a factor of two are observed between instances with low and high Inv value. We then show that for the randomized version of Quicksort, the number of element
swaps
performed is
provably
adaptive with respect to the measure Inv. More precisely, we prove that randomized Quicksort performs expected
O
(
n
(1 + log(1 + Inv/
n
))) element swaps, where Inv denotes the number of inversions in the input sequence. This result provides a theoretical explanation for the observed behavior and gives new insights on the behavior of Quicksort. We also give some empirical results on the adaptive behavior of Heapsort and Mergesort.
Publisher
Association for Computing Machinery (ACM)
Subject
Theoretical Computer Science
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献