A Multistage Linear Array Assignment Problem

R. K. Kincaid, D. M. Nicol, D. R. Shier and D. Richards
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R. K. Kincaid: The College of William and Mary, Williamsburg, Virginia
D. M. Nicol: The College of William and Mary, Williamsburg, Virginia
D. R. Shier: The College of William and Mary, Williamsburg, Virginia
D. Richards: University of Virginia, Charlottesville, Virginia

Operations Research, 1990, vol. 38, issue 6, 993-1005

Abstract: Implementation of certain algorithms on parallel computing architectures may involve partitioning contiguous elements into a fixed number of groups, each to be handled by a single processor. We wish to find an assignment of elements to processors that minimizes the sum of the maximum workloads experienced at each stage. This problem may be viewed as a multiobjective network optimization problem. Polynomially-bounded algorithms are developed for the case of two-stages, whereas the general problem, for an arbitrary number of stages, is shown to be NP-hard. Heuristic procedures are therefore proposed and analyzed for the general problem. Computational experience with one of the exact algorithms, incorporating certain pruning rules, is presented for a variety of test problems. Empirical results also demonstrate that one of the heuristic procedures is especially effective in practice.

Keywords: computers: parallel algorithms and workload balancing; networks; applications: multiobjective optimization (search for similar items in EconPapers)
Date: 1990
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