Allowable processing orders in the accelerated cascade algorithm

Abstract We deal with the ‘accelerated’ version (Bilde and Krarup, 1969) of the ‘all shortest distances’ Cascade Algorithm (Farbey et al., 1967). A set of weakest possible conditions on the processing-order for distance-matrix entries, under which the Bilde-Krarup acceleration remains valid, is determined. These conditions are weaker than those of Hu (1967) for the original algorithm, and in particular imply that the simple processing order of the original algorithm remains admissible for the accelerated version.