Fault-Tolerant Broadcasting in 2-D Wormhole-Routed Meshes

Abstract

In this paper, a fault-tolerant broadcast scheme in 2-D meshes with randomly generated faults is provided. This approach is based on an early work on time-step optimal broadcasting in square-shape fault-free 2-D meshes with optimal total communication distance (TCD). An extension to any rectangular-shape fault-free 2-D meshes is first given. The fault block model is used in which all faulty nodes in the system are contained in a set of disjoint blocks. The boundary lines of blocks divide the whole mesh into a set of fault-free polygons and a sequence of rectangular fault-free regions is derived from these polygons. The broadcast process is carried out at two levels: inter-region and intra-region. In the inter-region-level broadcast, the broadcast message is sent from a given source to a special node (called eye [1]) in each rectangular fault-free region. In the intra-region-level broadcast, the extended optimal fault-free broadcast is applied. Some analytical results are given including an upper bound of TCD.