Fault-tolerant meshes with minimal numbers of spares

This paper presents several techniques for adding fault-tolerance t o distributed memory parallel computers. More formally, given a target graph with n nodes, we create a fault-tolerant graph with n + k nodes such that given any set of k or fewer faulty nodes, the remaining graph is guaranteed to contain the target graph as a fault-free subgraph. As a result, any algorithm designed for the target graph will run with no slowdown in the presence of k or fewer node faults, regardless of their distribution. We present fault-tolerant graphs for target graphs which are 2dimensional meshes, tori, eight-connected meshes and hexagon.al meshes. In all cases our fault-tolerant graphs have smaller degree than any previously known graphs with the same properties.