Worst--Case Analysis of Weber's Algorithm

Christian Lavault (1) , Sidi Mohamed Sedjelmaci (1)

1 LIPN - Laboratoire d'Informatique de Paris-Nord

Recently, Ken Weber introduced an algorithm for finding the $(a,b)$-pairs satisfying $au+bv\equiv 0\pmod{k}$, with $0<|a|,|b|<\sqrt{k}$, 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.

Mots clés: Number theory; Integer greatest common divisor (GCD); Complexity analysis; Number theory.

Domaines: Calcul parallèle, distribué et partagé [cs.DC]; Mathématique discrète [cs.DM]; Complexité [cs.CC]; Combinatoire [math.CO]

Christian Lavault, Sidi Mohamed Sedjelmaci. Worst--Case Analysis of Weber's Algorithm. Information Processing Letters, 1999, 72 (3--4), pp.125--130. ⟨hal-00911130⟩