Abstract
Given a set of m tasks, where each task has an execution time and a subcube requirement, the Hypercube Scheduling Problem (HSP) is to find an assignment of tasks which minimizes the total completion time. The general HSP is known to be NP-hard. In this paper, we present a O(m log m) time algorithm for HSP when all the m tasks have the same execution time. We also present a polynomial time approximation algorithm which generates a solution within \(\frac{2}{{(1 + \tfrac{1}{{2^n }})}}\)of the optimal solution for the general HSP, where n is the hypercube dimension.
Research Supported in part by fellowships from the Faculty Research and Creative Activities Support Fund WMU-FRCASF 90-15 and WMU-FRCASF 89-225274, and by the National Science Foundation under grant USE-90-52346.
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© 1991 Springer-Verlag Berlin Heidelberg
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Boals, A., Gupta, A., Hashmi, J., Sherwani, N. (1991). An efficient approximation algorithm for hypercube scheduling. In: Dehne, F., Fiala, F., Koczkodaj, W.W. (eds) Advances in Computing and Information — ICCI '91. ICCI 1991. Lecture Notes in Computer Science, vol 497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54029-6_197
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DOI: https://doi.org/10.1007/3-540-54029-6_197
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