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A Lower Bound for the On-Line Preemptive Machine Scheduling with ℓ p Norm

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Computing and Combinatorics (COCOON 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5092))

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Abstract

We consider the on-line version of the preemptive scheduling problem that minimizes the machine completion time vector in the ℓ p norm (a direct extension of the l  ∞  norm: the makespan) on m parallel identical machines. We present a lower bound on the competitive ratio of any randomized on-line algorithm with respect to the general ℓ p norm. This lower bound amounts to calculating a (non-convex) mathematical program and generalizes the existing result on makespan. While similar technique has been utilized to provide the best possible lower bound for makespan, the proposed lower bound failed to achieve the best possible lower bound for general ℓ p norm (though very close), and hence revealing intricate and essential difference between the general ℓ p norm and the makespan.

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, China

    Tianping Shuai

  2. Faculty of Business Administration, University of New Brunswick, Canada

    Donglei Du

Authors
  1. Tianping Shuai
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  2. Donglei Du
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Xiaodong Hu Jie Wang

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© 2008 Springer-Verlag Berlin Heidelberg

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Shuai, T., Du, D. (2008). A Lower Bound for the On-Line Preemptive Machine Scheduling with ℓ p Norm. In: Hu, X., Wang, J. (eds) Computing and Combinatorics. COCOON 2008. Lecture Notes in Computer Science, vol 5092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69733-6_65

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  • DOI: https://doi.org/10.1007/978-3-540-69733-6_65

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69732-9

  • Online ISBN: 978-3-540-69733-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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