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Assuming a horizontally distributed computing system, formulations of the edge-failure and node-failure recovery problems from the standpoint of load-leveling are presented. The conditions for the existence of solutions to these problems are examined and simple algorithms are proposed for these problems. In connection with the node-failure recovery problem, the concept of a node-failure metric to characterize different possible solutions is introduced, exploiting the notion of the strength of processors. A possible application of the recovery methods in the context of reconfiguration of distributed database systems is suggested.