Worst-case analysis of Weber's GCD algorithm

Worst-case analysis of Weber's GCD algorithm

Recently, Ken Weber introduced an algorithm for finding the (a, b)-pairs satisfying au+ bv ≡ 0 (mod k), with 0< |a|, |b| < √ k, where (u, k) and (v, k) are coprime. It is based on Sorenson’s and Jebelean’s “k-ary reduction” algorithms. We provide a formula for N(k), the maximal number of iterations in the loop of Weber’s GCD algorithm.  1999 Elsevier Science B.V. All rights reserved.

Worst-Case Analysis of Weber's Algorithm

Recently, Ken Weber introduced an algorithm for finding the (a, b)-pairs satisfying au + bv ≡ 0 (mod k), with 0 < |a|, |b| < √ k, where (u, k) and (v, k) are coprime. It is based on Sorenson’s and Jebelean’s “k-ary reduction” algorithms. We provide a formula for N(k), the maximal number of iterations in the loop of Weber’s GCD algorithm.

Worst-Case Analysis of Read's Chromatic Polynomial Algorithm

The worst-case time-complexity of Read's edge-addition/contraction algorithm for computing the chromatic polynomial of an n-vertex graph is shown to be O(n2B(n)), where B(n) is the nth Bell number, which grows faster than cn for any c but slower than n!. The factor n2 can be reduced to n, and the space-complexity from O(n3) to O(n2), by storing in arrays the information needed to reverse each t...

Worst-case analysis of generalized heapsort algorithm revisited

In this paper we present a generalized heapsort algorithm and its worst-case complexity analysis. The weighted sum of the number of comparisons and movements has been defined as a measure of the complexity. Theoretical analysis suggests that, by this criterion, 3-heap should be optimal in the worst case, contradicting the findings of A. Paulik (Paulik, A., 1990, Worst-case analysis of a general...

The Worst Case Analysis of Algorithm on Multiple Stacks Manipulation