Abstract
Fast implementations of the kink-jump-crankshaft and Berg-Foerster-Aragao de Carvalho-Caracciolo-Froehlich (BFACF) algorithms are discussed and applied to the study of topologically knotted polymers. The effect of knots on the size scaling laws of polymers is investigated. Finally, a comparison between the size scaling of the kink-jump-crankshaft and BFACF alogorithms is made