Heuristic Algorithms for Task Assignment in Distributed Systems
IEEE Transactions on Computers
Multiprocessor Scheduling with the Aid of Network Flow Algorithms
IEEE Transactions on Software Engineering
IEEE Transactions on Software Engineering
The assignment of computational tasks among processors in a distributed system
AFIPS '81 Proceedings of the May 4-7, 1981, national computer conference
An algorithm for the multiprocessor assignment problem
Operations Research Letters
Task assignment in heterogeneous computing systems
Journal of Parallel and Distributed Computing
The task allocation problem with constant communication
Discrete Applied Mathematics
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The Task Assignment problem consists of assigning tasks to processors in order to minimize the sum of execution times and communication costs. It is equivalent to the Multiway Cut problem, where for a weighted graph with specified vertices S = {s"i,...,s"N} one has to select a set of edges of minimal weight that separates the s"i s. A problem's size can be reduced by Stone's observation that vertices in the same components as s"1 in a minimal (s"1, S - s"1) cut remain so in an optimal multiway cut. Hence the optimal assignment of a task to a processor might sometimes be determined by solving an auxiliary two processor problem, which amounts to a max flow computation. In this paper we show that the same property holds in a different two cut-two processor problem, and at least as many tasks are thus assigned as through Stone's procedure. Computational results show that the improvement is significant although for large problems no reduction is to be expected. The method can be extended to identify tasks whose optimal assignment is restricted to be in a subset of the processors.