Fault‐tolerant processor interconnection networks

Abstract

AbstractAs suitable topology for interconnection networks of multiprocessors, De Bruijn graphs have been proposed and a number of investigations have been conducted on their fault tolerance. A De Bruijn graph is a directed graph with maximum degree d (the maximum number of links that can be connected to one processor), diameter k (maximum number of repeaters between two processors) and number of nodes dk (number of processors). A Kautz graph is a directed graph with maximum degree d, diameter k and number of nodes dk + dk‐1. Both have the smallest diameter among the graphs with maximum degree d. This paper proves the following: (1) If d ‐2 nodes in a De Bruijn graph are removed (if d ‐2 processors are faulty), its diameter becomes d + 1, which is only 1 larger than the original diameter. (2) If d ‐3 nodes in a Kautz graph are removed, its diameter becomes k + 1 and if d ‐1 nodes are removed, the diameter is k + 2 or less, which is at most 2 larger than the original diameter. (3) The values of (1) and (2) are at most 1 larger than the lower bound under the limitation of degree d, (4) A fault‐tolerant routing algorithm can be realized easily. This algorithm is better than any existing algorithm because of its short routes.