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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;
On the partition function of a finite set
"... Let A = {a1,a2,...,ak} be a set of k relatively prime positive integers. Let p A (n) denote the partition function of n with parts in A, thatis,p A is the number of partitions of n with parts belonging to A. We survey some known results on p A (n) for general k, and then concentrate on the cases k = ..."
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Let A = {a1,a2,...,ak} be a set of k relatively prime positive integers. Let p A (n) denote the partition function of n with parts in A, thatis,p A is the number of partitions of n with parts belonging to A. We survey some known results on p A (n) for general k, and then concentrate on the cases k = 2 (where the exact value of p A (n) isknownfor all n), and the more interesting case k = 3. We also describe an approach using the cycle indicator formula. Let A = {a, b, c}, wherea, b, c are pairwise relatively prime. It has