The triangle scheduling problem

Christoph Dürr (), Zdeněk Hanzálek (), Christian Konrad (), Yasmina Seddik (), René Sitters (), Óscar C. Vásquez () and Gerhard Woeginger ()
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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

Journal of Scheduling, 2018, vol. 21, issue 3, No 3, 305-312

Abstract: 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.

Keywords: Scheduling; Mixed-criticality; Packing (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10951-017-0533-1

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