Jet transition values for the anti-$k_{\mathrm{\perp }}$ algorithm

We define jet transition values for the anti-$k_{\mathrm{\perp }}$ algorithm for both hadron and $e^{+}{e}^{-}$ colliders. We show how these transition values can be computed and how they can be used to improve the performance of clusterization when jet resolution parameters are varied over a larger set of values. Finally we present a simple performance test to illustrate the behavior of the new method compared to the original one.