A Comparative Study of X-Tree, Pyramid and Related Machines

configuration in which two RAMS are connected to each other through a single communication link and then calculating the number of crossing sequences for this configuration. (For a detailed discussion, see Aho et. ai’s paper [AUY83].) Both techniques have a serious drawback : they do not take into account any but the simplest aspects of the network topology (like the diameter, the bisection width etc.). Fortunately, these techniques work well for most known parallel networks (like the shuffle exchange network, the Cube Connected Cycles, meshes etc.) but they yield only trivial bounds for the X-tree and the pyramid machines. Our lower bound technique incorporates the network topology and yields non-trivial bounds for these networks. However, it works only for conservative flow algorithms (described later), and its generalization for the most general algorithms remains unresolved. Models of various networks are described in section & our main contributions are summarized below. For the sake of brevity, we list most propositions and theorems without proofs; the proofs for remaining propositions will appear in the final version of the paper.