Characterization, testing and reconfiguration of faults in mesh networks

Achieving fault-tolerance through incorporation of redundancy and reconfiguration is quite common. The distribution of faults can have several impacts on the effectiveness of any reconfiguration scheme; in fact, patterns of faults occurring at strategic locations may render an entire VLSI system unusable regardless of its component redundancy and its reconfiguration capabilities. Such fault patterns are called catastrophic fault patterns (CFPs). In this paper, we characterize catastrophic fault patterns in mesh networks when the links are bidirectional or unidirectional. We determine the minimum number of faults required for a fault pattern to be catastrophic. We consider the problem of testing whether a fault pattern is catastrophic. When a fault pattern is not catastrophic we study the problem of finding optimal reconfiguration strategies, where optimality is with respect to either the number of processing elements in the reconfigured network (the reconfiguration is optimal if such a number is maximized) or the number of bypass links to activate in order to reconfigure the array (the reconfiguration is optimal if such a number is minimized). The problem of finding a reconfiguration strategy that is optimal with respect to the size of the reconfigured network is NP-complete, when the links are bidirectional, while it can be solved in polynomial time, when the links are unidirectional. Considering optimality with respect to the number of bypass links to activate, we provide algorithms which efficiently find an optimal reconfiguration. r 2006 Elsevier B.V. All rights reserved.