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Inapproximability and Polynomial-Time Approximation Algorithm for UET Tasks on Structured Processor Networks

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  • M. Bouznif
  • R. Giroudeau

Abstract

We investigate complexity and approximation results on a processor networks where the communication delay depends on the distance between the processors performing tasks. We then prove that there is no heuristic with a performance guarantee smaller than 4/3 for makespan minimization for precedence graph on a large class of processor networks like hypercube, grid, torus, and so forth, with a fixed diameter 𠛿 ∈ ℕ . We extend complexity results when the precedence graph is a bipartite graph. We also design an efficient polynomial-time 𠑂 ( 𠛿 2 ) -approximation algorithm for the makespan minimization on processor networks with diameter 𠛿 .

Suggested Citation

  • M. Bouznif & R. Giroudeau, 2011. "Inapproximability and Polynomial-Time Approximation Algorithm for UET Tasks on Structured Processor Networks," Advances in Operations Research, Hindawi, vol. 2011, pages 1-20, June.
    • Handle: RePEc:hin:jnlaor:476939
    DOI: 10.1155/2011/476939
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