Reconfiguration in Fault-Tolerant 3d Meshes

Abstract

The [Formula: see text] track model for fault tolerant 2D processor arrays is extended to 3D mesh architectures. Non-intersecting, continuous, straight and non-near miss compensation paths are considered. It is shown that when six directions in the 3D mesh are allowed for compensation paths, then switches with 13 states are needed to preserve the 3D mesh topology after faults. The number of switch states reduces to 7 if only 3 directions are allowed for compensation paths. It is also shown that switch reconfiguration after faults is local in the sense that the state of each switch is uniquely determined by the states of the 2 processors connected to it.