Necessary and Sufficient Conditions for Deadlock-free Networks

In this paper we develop a new and generic theory about the necessary and sufficient conditions for deadlock-free routing in the interconnection networks An extension of the channel dependency graph described by Dally is defined, the channel dynamic dependency graph. The main achievement of this new concept is consecuence of introducing the concept of time and the flow control function in its definition. Our theory remains valid for different routing and flow control functions showing that even if Duato 's theorem conditions are not fulfilled the network can be deadlock-free. Index Terms - Multicomputer networks, deadlock, flow control, routing 1 Introduction Many recent experimental and commercial parallel computers [13] use direct networks for low latency, high bandwidth interprocessor communication. The typical direct networks are k-ary n-cube structures [7], which are cubes with dimension n and k nodes in each dimension. Rings, meshes and tori are included in this class of networ..

A Flow Control Mechanism to Avoid Message Deadlock in

In this paper we propose a flow control algorithm for k-ary n-cube networks which avoids the deadlock problems without using virtual channels. Some basic definitions and theorems are proposed in order to establish the necessary and sufficient conditions to verify that an algorithm is deadlock-free. Our proposal is based on a restriction of the virtual cut-through flow control rather than of the routing algorithm and it can be applied both over central buffers or edge buffers. A minimum free buffer space of two packets is required. The implementation complexity of the router, according to Chien's model, is much easier and faster than using virtual channels. Network simulations considering the router complexity show the performance achieved by this new algorithm. The results display a latency improvement of 20% to 35% compared with the use of virtual channels depending on the load of the network. 1 Introduction Many recent experimental and commercial parallel computers [15] [17] use d..