Ming-Hour Yang

An Euler-path-based multicasting model for wormhole-routed networks with multi-destination capability

Recently, wormhole routers with multi-destination capability have been proposed to support fast multicast in a multi-computer network. In this paper, we develop a new multicasting model for such networks based on the concept of Euler path/circuit in graph theory. The model can support multiple concurrent multicasts freely from deadlock and can be applied to any network which is Eulerian or is Eulerian after some links being removed. No virtual channels are needed. In particular, we demonstrate the potential of this model by showing its fault-tolerant capability in supporting multicasting in the currently popular torus/mesh topology of any dimension with regular fault patterns (such as single node, block, L-shape, +-shape, U-shape, and H-shape) and even irregular fault patterns. The result has improved over existing fault-tolerant routing algorithms for meshes/tori in at least one of the following aspects: the number of faults tolerable, the shape of fault patterns, the number of deactivated healthy nodes, the requirement of support of virtual channels, and the range of network topology acceptable.

An Euler-path-based multicasting model for wormhole-routed networks: its applications to damaged 2D Tori and meshes

We develop a new multicasting model for wormhole-routed networks based on the concept of Euler path in graph theory. The model can support multiple multicasts freely from deadlock and can be applied to any network which is Eulerian or is Eulerian after some links being removed. We demonstrate the power of this model by showing its fault-tolerant capability in supporting multicasting in a damaged 2-D torus/meshes with regular fault patterns (such as a single node, block, L-shape, +-shape, U-shape, and H-shape). In this regard, it is the first known multicasting algorithm in the literature with such strong fault-tolerant capability.

Achieving fault-tolerant multicast in injured wormhole-routed tori and meshes based on Euler path construction

Recently, wormhole routers with multidestination capability have been proposed to support fast multicast in a multicomputer network. To avoid communication deadlock, existing results have proposed to construct a Hamilton path, Euler path, trip, or their variants in the network, perhaps with some degree of support of virtual channels. In this paper, we identify that a network which is itself Eulerian or is Eulerian after some links are removed, can enjoy the multidestination capability without support of virtual channels. From this definition, we then develop several techniques to achieve fault-tolerant multicast in a torus/mesh of any dimension with regular fault patterns (such as single node, block, L-shape, T-shape, +-shape, U-shape, and H-shape) and even irregular fault patterns. The result improves over existing results on the requirement of support of virtual channels and fault-tolerant capability. Simulation results on tori are presented.

Multi-node multicast in three and higher dimensional wormhole tori and meshes with load balance

This paper considers the multi-node multicast problem in a multi-dimensional wormhole-routed torus/mesh, where there are an arbitrary number of source nodes each intending to multicast a message to an arbitrary set of destinations. This problem requires a large amount of bandwidth, and thus typically incurs heavy contention and congestion. Evenly balancing the traffic load around the network is a critical issue to achieve good performance. We show how to use a network-partitioning approach to achieve this goal. Simulation results show significant improvement over existing results in 3D tori and meshes. This work is an extension of our earlier work (2000) from 2D tori/meshes to higher dimensional ones.