A General Method for Maximizing the Error-Detecting Ability of Distributed Algorithms

The bound on component failures and their spatial distribution govern the fault tolerance of any candidate error-detecting algorithm. For distributed memory mul-tiprocessors, the speciic algorithm and the topology of the processor intercon-nection network deene these bounds. This paper introduces the maximal fault index, derived from the system topology and local communication patterns, to demonstrate how a maximal number of simultaneous (Byzantine) component failures can be tolerated for a particular interconnection network and error-detecting algorithm. The index is used to design a fault-tolerant mapping of processes to processor groups such that the error-detecting ability of the algorithm is preserved for certain multiple simultaneous processor failures. 1 X X b) Overlapping communication environments with non-interfering faults a) A communication environment c) Overlapping communication environments with interfering faults X X Figure 1: Communication environments.