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A greedy approximation algorithm for minimum-gap scheduling

Author

Listed:
  • Marek Chrobak

    (University of California)

  • Uriel Feige

    (The Weizmann Institute)

  • Mohammad Taghi Hajiaghayi

    (University of Maryland)

  • Sanjeev Khanna

    (University of Pennsylvania)

  • Fei Li

    (George Mason University)

  • Seffi Naor

    (Technion)

Abstract

We consider scheduling of unit-length jobs with release times and deadlines, where the objective is to minimize the number of gaps in the schedule. Polynomial-time algorithms for this problem are known, yet they are rather inefficient, with the best algorithm running in time $$O(n^4)$$ O ( n 4 ) and requiring $$O(n^3)$$ O ( n 3 ) memory. We present a greedy algorithm that approximates the optimum solution within a factor of 2 and show that our analysis is tight. Our algorithm runs in time $$O(n^2 \log n)$$ O ( n 2 log n ) and needs only O(n) memory. In fact, the running time is $$O(n (g^*+1)\log n)$$ O ( n ( g ∗ + 1 ) log n ) , where $$g^*$$ g ∗ is the minimum number of gaps.

Suggested Citation

  • Marek Chrobak & Uriel Feige & Mohammad Taghi Hajiaghayi & Sanjeev Khanna & Fei Li & Seffi Naor, 2017. "A greedy approximation algorithm for minimum-gap scheduling," Journal of Scheduling, Springer, vol. 20(3), pages 279-292, June.
    • Handle: RePEc:spr:jsched:v:20:y:2017:i:3:d:10.1007_s10951-016-0492-y
    DOI: 10.1007/s10951-016-0492-y
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    Cited by:

    1. Marek Chrobak & Mordecai Golin & Tak-Wah Lam & Dorian Nogneng, 2021. "Scheduling with gaps: new models and algorithms," Journal of Scheduling, Springer, vol. 24(4), pages 381-403, August.

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