Routing Function and Deadlock Avoidance in a Star Graph Interconnection Network

In this paper the properties of paths in a star graph are investigated through the analysis of the corresponding star transposition tree. The general algebraic expression for all shortest paths between any two nodes (routing function) is found, and it is shown that every shortest path consists of a number of subpaths which can be combined in an arbitrary order or even mutually nested. Further, due to the known routing function the deadlock problem is solved using the method of virtual channels. A minimal deterministic routing algorithm is developed which recognizes the structure of the path by extracting subpaths and allows optimal adaptive management of virtual channels. Finally, based on the sufficient number of virtual channels, the minimal fully adaptive routing algorithm is suggested which offers an opportunity to reroute the message a number of times, while maintaining the shortest path between two nodes.