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The triangle scheduling problem

Author

Listed:
  • Christoph Dürr

    (Sorbonne Universités)

  • Zdeněk Hanzálek

    (Czech Technical University in Prague)

  • Christian Konrad

    (University of Warwick)

  • Yasmina Seddik

    (Czech Technical University in Prague)

  • René Sitters

    (Vrije Universiteit)

  • Óscar C. Vásquez

    (University of Santiago of Chile)

  • Gerhard Woeginger

    (RWTH Aachen University)

Abstract

This paper introduces a novel scheduling problem, where jobs occupy a triangular shape on the time line. This problem is motivated by scheduling jobs with different criticality levels. A measure is introduced, namely the binary tree ratio. It is shown that the Greedy algorithm solves the problem to optimality when the binary tree ratio of the input instance is at most 2. We also show that the problem is unary NP-hard for instances with binary tree ratio strictly larger than 2 and provide a quasi-polynomial time approximation scheme. The approximation ratio of Greedy on general instances is shown to be between 1.5 and 1.05.

Suggested Citation

  • Christoph Dürr & Zdeněk Hanzálek & Christian Konrad & Yasmina Seddik & René Sitters & Óscar C. Vásquez & Gerhard Woeginger, 2018. "The triangle scheduling problem," Journal of Scheduling, Springer, vol. 21(3), pages 305-312, June.
    • Handle: RePEc:spr:jsched:v:21:y:2018:i:3:d:10.1007_s10951-017-0533-1
    DOI: 10.1007/s10951-017-0533-1
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