Results 1 
6 of
6
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 ..."
Abstract

Cited by 31 (0 self)
 Add to MetaCart
(Show Context)
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 = ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
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
HOW TO CHANGE COINS, M&M’S, OR CHICKEN NUGGETS: THE LINEAR DIOPHANTINE PROBLEM OF FROBENIUS
"... Let’s imagine that we introduce a new coin system. Instead of using pennies, nickels, dimes, and quarters, let’s say we agree on using 4cent, 7cent, 9cent, and 34cent coins. The reader might point out the following flaw of this new system: certain amounts cannot be exchanged, for example, 1, 2, ..."
Abstract
 Add to MetaCart
(Show Context)
Let’s imagine that we introduce a new coin system. Instead of using pennies, nickels, dimes, and quarters, let’s say we agree on using 4cent, 7cent, 9cent, and 34cent coins. The reader might point out the following flaw of this new system: certain amounts cannot be exchanged, for example, 1, 2, or 5 cents. On the other hand, this deficiency makes our new coin system more
The Frobenius Problem in a Free Monoid
, 2008
"... Given positive integers c1, c2,..., ck with gcd(c1, c2,..., ck) = 1, the Frobenius problem (FP) is to compute the largest integer g(c1, c2,..., ck) that cannot be written as a nonnegative integer linear combination of c1, c2,..., ck. The Frobenius problem in a free monoid (FPFM) is a noncommu ..."
Abstract
 Add to MetaCart
Given positive integers c1, c2,..., ck with gcd(c1, c2,..., ck) = 1, the Frobenius problem (FP) is to compute the largest integer g(c1, c2,..., ck) that cannot be written as a nonnegative integer linear combination of c1, c2,..., ck. The Frobenius problem in a free monoid (FPFM) is a noncommutative generalization of the Frobenius problem. Given words x1, x2,..., xk such that there are only finitely many words that cannot be written as concatenations of words in {x1, x2,..., xk}, the FPFM is to find the longest such words. Unlike the FP, where the upper bound g(c1, c2,..., ck) ≤ max1≤i≤k c2i is quadratic, the upper bound on the length of the longest words in the FPFM can be exponential in certain measures and some of the exponential upper bounds are tight. For the 2FPFM, where the given words