Using Golomb rulers for optimal recovery schemes in fault tolerant distributed computing

Clusters and distributed systems offer fault tolerance and high performance through load sharing. When all computers are up and running, we would like the load to be evenly distributed among the computers. When one or more computers break down the load on these computers must be redistributed to other computers in the cluster. The redistribution is determined by the recovery scheme. The recovery scheme should keep the load as evenly distributed as possible even when the most unfavorable combinations of computers break down, i.e. we want to optimize the worst-case behavior. In this paper we define recovery schemes, which are optimal for a number of important cases. We also show that the problem of finding optimal recovery schemes corresponds to the mathematical problem called Golomb rulers. These provide optimal recovery schemes for up to 373 computers in the cluster.