Optimal task assignment in linear array networks

The problem of assigning tasks to the processors of a distributed computing system such that the sum of execution and communication costs is minimized is discussed. This problem is known to be NP-complete in the general case, and thus intractable for systems with a large number of processors. H.S. Stone´s (1977) network flow approach for a two-processor system is extended to the case for a linear array of any number of processors. The task assignment problem for a linear array network is first transformed into the two-terminal network flow problem, and then solved by applying the Goldberg-Tarjan (1987) network flow algorithm in time no worse than O(n²m ³ log n), where n and m are the number of processors and the number of tasks, respectively