Configuring Group-Multicast Rings With Randomly Selected Nodes On Binary N-Cubes

Abstract

In this paper we present a systematic method of configuring group-multicast rings with randomly selected nodes on binary n-cube multiprocessors. The method configures rings only with disjoint links so that the selected nodes can perform multicast communication without messages collision. Binary n-cube multiprocessors are typically one-port architectures, which allow a processor node to send or receive only one message at a time. Being capable of pipelining messages throughout nodes, rings offer a practical solution to perform group multicast operations on one-port architectures. The basic idea behind our proposed method is to repeatedly merge small rings to form larger rings. Once a multicast ring is configured, messages can circulate around the ring without incurring link contentions. We begin with introducing a basic network model which specifies path routing on n-cubes. Then we present some preliminary results regarding properties of disjoint paths. The concept of the proposed method is described. Finally, the method is formally presented and its correctness is verified. The proposed method presents two unique features. First, it guarantees that the physical distance between adjacent nodes is limited to n links on an n-cube. Secondly, it uses only a single dimension order to route messages across the links towards their respective destinations.