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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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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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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 ...
Parallel sorting on ILLIAC array processor, in
 Proc. of the 7th Conference on 7th WSEAS International Conference on Systems Theory and Scientific Computation
, 2007
"... Abstract: Nowadays, we need to speed up solving computer problems such as sorting. Because of limitations in processor's speed, using parallel algorithms is inevitable. In parallel algorithms, because of cost limitations and architecture complexity, it's not suitable to increase the number ..."
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Abstract: Nowadays, we need to speed up solving computer problems such as sorting. Because of limitations in processor's speed, using parallel algorithms is inevitable. In parallel algorithms, because of cost limitations and architecture complexity, it's not suitable to increase the number of processors to speed up. This is also infeasible where we have plenty of data. In this paper we issue a new sorting algorithm. The algorithm is implemented on ILLIAC architecture. The aim of issued algorithm is to reduce total cost of sorting with a trade off between the number of processors and execution time.
A SuperLogarithmic Lower Bound for ShuffleUnshuffle Sorting Networks
, 1994
"... Shuffleunshuffle sorting networks are a class of comparator networks whose structure maps efficiently to the hypercube and any of its bounded degree variants. Recently, ninput shuffleunshuffle sorting networks with depth2O(plglgn)lgn have been discovered. These networks are the only known sorting ..."
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Shuffleunshuffle sorting networks are a class of comparator networks whose structure maps efficiently to the hypercube and any of its bounded degree variants. Recently, ninput shuffleunshuffle sorting networks with depth2O(plglgn)lgn have been discovered. These networks are the only known sorting networks of depth o(lg2n) that are not based on expanders, and their existence raises the question of whether a depth of O(lgn) can be achieved by any shuffleunshuffle sorting network. In this paper, we resolve this question by establishing lglglgnlower bound on the depth of anyninput shuffleunshuffle sorting network. Our lower bound can be extended to certain restricted classes of nonoblivious sorting algorithms on hypercubic machines.