Self-routing least common ancestor networks

Fat-trees, KYKLOS, baseline and SW-banyan networks, and the TRAC and CM-5 networks belong to a family of networks called least-common-ancestor networks (LCANs). In this paper, attention is restricted to LCANs with identical switches and a uniform stage interconnect. The least common ancestor of two nodes (PEs), A and B, is the node at greatest depth that counts A and B among its descendants: this node corresponds to an LCA switch. Given a source-destination pair, communication progresses upwards to an LCA switch; the stage that it belongs to is called the LCA level. Then, routing returns downwards to the destination. Source-destination pairs are connected using as few stages as their degree of mutual locality permits. Network parameters that facilitate this routing are shown.<>