Approximate algorithms for partitioning problems (original) (raw)

Abstract

We consider the problem of optimally assigning the modules of a parallel/pipelined program over the processors of a multiple processor system under certain restrictions on the interconnection structure of the program as well as the multiple computer system. We show that for a variety of such problems, it is possible to find if a partition of the modular program exists in which the load on any processor is whithin a certain bound. This method when combined with a binary search over a fixed range, provides an optimal solution to the partitioning problem.

The specific problems we consider are partitioning of (1) a chain structured parallel program over a chain-like computer system, (2) multiple chain-like programs over a host-satellite system, and (3) a tree structured parallel program over a host-satellite system.

For a problem with_N_ modules and_M_ processors, the complexity of our algorithm is no worse than_O(M_log(N)log(W T/∈)), where_W_ T is the cost of assigning all modules to one processors, and ∈ the desired accuracy. This algorithm provides an improvement over the recently developed best known algorithm that runs in_O(MN_log(N)) time.

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Author notes

  1. Mohammad Ashraf Iqbal
    Present address: Department of EE-Systems, University of Southern California, 90007, Los Angeles, California

Authors and Affiliations

  1. Department of Electrical Engineering, University of Engineering and Technology, Lahore, Pakistan
    Mohammad Ashraf Iqbal

Authors

  1. Mohammad Ashraf Iqbal

Additional information

This Research was supported by a grant from the Division of Research Extension and Advisory Services, University of Engineering and Technology Lahore, Pakistan. Further support was provided by NASA Contracts NAS1-17070 and NAS1-18107 while the author was resident at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, Virginia, USA.

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Iqbal, M.A. Approximate algorithms for partitioning problems.Int J Parallel Prog 20, 341–361 (1991). https://doi.org/10.1007/BF01407812

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