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<p>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(n/sup 2/m/sup 3/ log n), where n and m are the number of processors and the number of tasks, respectively.</p>
optimal task assignment; linear array networks; distributed computing system; communication costs; NP-complete; network flow approach; task assignment; two-terminal network flow problem; computational complexity; computer networks; distributed processing.

M. Kim, D. Lee and C. Lee, "Optimal Task Assignment in Linear Array Networks," in IEEE Transactions on Computers, vol. 41, no. , pp. 877-880, 1992.
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