Abstract
The problem of mapping tasks to processors in a multi-processor system in order to minimize communication time is addressed. The following assumptions about the problem are made. Communication among tasks follows a static pattern; all processors are identical; and all tasks are similar. We formulate the problem as a quadratic assignment problem (QAP). Two significant features of such a QAP are its large size and sparseness.
A heuristic algorithm based on tabu search is developed and implemented in parallel on the connection machine CM-2. In our parallel implementation two levels of parallelism are employed. First, the candidate tasks to be swapped are identified in parallel. Second, more than one pair of tasks are swapped in a single iteration. The computed effect of a single swapping is based on the assumption that no other swapping takes place in the current iteration. When performing multiple swaps, the cumulative effect of the swapping may not correspond to the sum of the individual effects. We show how this could lead to an inferior performance and illustrate the elements of our heuristic that makes it robust under these circumstances. Computations are performed on data of size up to 64000 tasks.
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References
J. Chaktapani and J. Skorin-Kapov, 1993. Massively parallel tabu search for the quadratic assignment problem. Annals of Operations Research, 41:327–341.
D.E. Dahl, 1990. Mapping and compiled communication on the connection machine system. In Proceedings of the Fifth Distributed Memory Comput ing Conference, 756–766. IEEE Computer Society.
G. Finke, R.E. Burkard, and F. Rendl, 1987. Quadratic assignment prob lems. Annals of Discrete Mathematics, 31:61–82.
G. Fox et al, 1988. Solving Problems on Concurrent Processors. Prentice Hall.
F. Glover, 1989. Tabu search — part I. ORSA Journal on Computing, l(3):190–206.
F. Glover, 1990. Tabu search — part II. ORSA Journal on Computing, 2(l):4–32.
S.W. Hammond, 1992. Mapping Unstructured Grid Computations to Mas sively Parallel Computers. PhD thesis, Rensselaer Polytechnic Institute, Troy, New York.
W. D. Hillis, 1985. The Connection Machine. The MIT Press.
C.T. Ho and S.L. Johnson, 1989. Embedding meshes in boolean cubes by graph decomposition. Journal of Parallel and Distributed Computing.
Behzad Kamgar-Parsi, J.A. Gualtieri, J.E. Devaney, and Behrooz Kamgar Parsi, 1990. Clustering with neural networks. Biological Cybernetics, 63:201–208.
J.P. Kelly, M. Laguna, and F. Glover, 1991. A study of diversification strategies for the quadratic assignment problem, to appear in Computers and Operations Research.
A. Pothen, H.D. Simon, and Kang-Pu Liou, 1990. Partitioning sparse matrices with eigenvectors of graphs. SIAM Journal of Matrix Analysis and Applications, 11(3):430–452.
R. Shapiro, 1992. Private Communication.
J. Skorin-Kapov, 1990. Tabu search applied to the quadratic assignment problem. ORSA Journal on Computing, 2(l):33–45.
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© 1995 Springer Science+Business Media New York
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Chakrapani, J., Skorin-Kapov, J. (1995). Mapping Tasks to Processors to Minimize Communication Time in a Multiprocessor System. In: Nash, S.G., Sofer, A., Stewart, W.R., Wasil, E.A. (eds) The Impact of Emerging Technologies on Computer Science and Operations Research. Operations Research/Computer Science Interfaces Series, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2223-2_3
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DOI: https://doi.org/10.1007/978-1-4615-2223-2_3
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