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Analysis of Shellsort and related algorithms
 ESA ’96: Fourth Annual European Symposium on Algorithms
, 1996
"... This is an abstract of a survey talk on the theoretical and empirical studies that have been done over the past four decades on the Shellsort algorithm and its variants. The discussion includes: upper bounds, including linkages to numbertheoretic properties of the algorithm; lower bounds on Shellso ..."
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Cited by 26 (0 self)
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This is an abstract of a survey talk on the theoretical and empirical studies that have been done over the past four decades on the Shellsort algorithm and its variants. The discussion includes: upper bounds, including linkages to numbertheoretic properties of the algorithm; lower bounds on Shellsort and Shellsortbased networks; averagecase results; proposed probabilistic sorting networks based on the algorithm; and a list of open problems. 1 Shellsort The basic Shellsort algorithm is among the earliest sorting methods to be discovered (by D. L. Shell in 1959 [36]) and is among the easiest to implement, as exhibited by the following C code for sorting an array a[l],..., a[r]: shellsort(itemType a[], int l, int r) { int i, j, h; itemType v;
Lower Bounds for Shellsort
 In Proceedings of the 33rd Annual IEEE Symposium on Foundations of Computer Science
, 1997
"... We show lower bounds on the worstcase complexity of Shellsort. In particular, we give a fairly simple proof of an \Omega\Gamma n lg 2 n=(lg lg n) 2 ) lower bound for the size of Shellsort sorting networks, for arbitrary increment sequences. We also show an identical lower bound for the running ..."
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Cited by 13 (4 self)
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We show lower bounds on the worstcase complexity of Shellsort. In particular, we give a fairly simple proof of an \Omega\Gamma n lg 2 n=(lg lg n) 2 ) lower bound for the size of Shellsort sorting networks, for arbitrary increment sequences. We also show an identical lower bound for the running time of Shellsort algorithms, again for arbitrary increment sequences. Our lower bounds establish an almost tight tradeoff between the running time of a Shellsort algorithm and the length of the underlying increment sequence. Proposed running head: Lower Bounds for Shellsort. Contact author: Prof. Greg Plaxton, Department of Computer Science, University of Texas at Austin, Austin, Texas 787121188. 1 Introduction Shellsort is a classical sorting algorithm introduced by Shell in 1959 [15]. The algorithm is based on a sequence H = h 0 ; : : : ; hm\Gamma1 of positive integers called an increment sequence. An input file A = A[0]; : : : ; A[n \Gamma 1] of elements is sorted by performing an ...
Asymptotic Complexity from Experiments?  A Case Study for Randomized Algorithms
 IN PROCEEDINGS OF THE 4TH WORKSHOP OF ALGORITHMS AND ENGINEERING (WAE'00
, 2000
"... In the analysis of algorithms we are usually interested in obtaining closed form expressions for their complexity, or at least asymptotic expressions in O()notation. Unfortunately, there are fundamental reasons why we cannot obtain such expressions from experiments. This paper explains how we can ..."
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Cited by 4 (2 self)
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In the analysis of algorithms we are usually interested in obtaining closed form expressions for their complexity, or at least asymptotic expressions in O()notation. Unfortunately, there are fundamental reasons why we cannot obtain such expressions from experiments. This paper explains how we can at least come close to this goal using the scientific method. Besides the traditional role of experiments as a source of preliminary ideas for theoretical analysis, experiments can test falsifiable hypotheses obtained by incomplete theoretical analysis. Asymptotic behavior can also be deduced from stronger hypotheses which have been induced from experiments. As long as a complete mathematical analysis is impossible, well tested hypotheses may have to take their place. Several