Allocating programs containing branches and loops within a multiple processor system
IEEE Transactions on Software Engineering
Allocating Modules to Processors in a Distributed System
IEEE Transactions on Software Engineering
Multiprocessor Scheduling with the Aid of Network Flow Algorithms
IEEE Transactions on Software Engineering
IEEE Transactions on Software Engineering
An algorithm for the multiprocessor assignment problem
Operations Research Letters
Approximating a class of classification problems
Efficient Approximation and Online Algorithms
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The Task Assignment Problem (TAP) arises in distributed computing environments and is a relaxed version of the Quadratic Assignment Problem (QAP). In this paper we present a new approach to the QAP which relies on the relationship between the two problems. First, by using the TAP, Lagrangian relaxation lower bounds are obtained for QAPs whose underlying flow graph is a k-tree, a generalization of ordinary trees. Second, for QAPs on arbitrary flow graphs the TAP solution is combined with the well-known Gilmore-Lawler procedure to get an improved bound. Methods to speed-up the branch and bound search are presented, based on the sequence in which the machines are examined and on the use of the linear assignment problem. Finally, we report on our computational results.