A linear-time algorithm for computing the diameters of the incomplete WK-recursive networks

The WK-recursive networks, which were originally proposed by Vecchia and Sanges, have suffered from the rigorous restriction on the number of nodes. Like the other incomplete networks, the incomplete WK-recursive networks have been proposed to relieve this restriction. In this paper, it is first shown that the structures of the incomplete WK-recursive networks are conveniently represented with multistage graphs. This representation can provide a uniform look at the incomplete WK-recursive networks. With its help, a linear-time algorithm using the prune-and-search technique is presented for computing the diameters of the incomplete WK-recursive networks.