Reconfigurability and Reliability of Systolic/Wavefront Arrays

AbstructIn this paper, we study fault-tolerant redundant structures for maintaining reliable arrays. In particular, we assume the desired array (application graph) is embedded in a certain class of regular, bounded-degree graphs called dynamic graphs. We define the degree of reconfigurability D R , and D R with distance D R d , of a redundant graph. When D R (respectively, D R d ) is independent of the size of the application graph, we say the graph is finitely reconfigurable, F R (respectively, locally reconfigurable, LR). We show that D R provides a natural lower bound on the time complexity of any distributed reconfiguration algorithm and that there is no difference between being F R and L R on dynamic graphs. We then show that if we wish to maintain both local reconfigurability and a fixed level of reliability, a dynamic graph must be of dimension at least one greater than the application graph. Thus, for example, a one-dimensional systolic array cannot be embedded in a one-dimensional dynamic graph without sacrificing either reliability or locality of reconfiguration.