The triangle scheduling problem

Christoph Dürr*, Zdeněk Hanzálek, Christian Konrad, Yasmina Seddik, R.A. Sitters, Óscar C. Vásquez, Gerhard Woeginger

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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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.

Original languageEnglish
Pages (from-to)305–312
Number of pages8
JournalJournal of Scheduling
Volume21
Issue number3
Early online date18 May 2017
DOIs
Publication statusPublished - Jun 2018

Funding

This work is partially supported by PHC VAN GOGH 2015 Projet 33669TC, the Grants FONDECYT 11140566, ANR-15-CE40-0015, and by the Project AI and Reasoning CZ.02.1.01/0.0/0.0/15_003/0000466 as well as by the European Regional Development Fund. Christian Konrad is supported by Icelandic Research Fund Grants 120032011 and 152679-051.

FundersFunder number
Providence Health Care33669TC
Icelandic Centre for Research120032011, 152679-051
Fondo Nacional de Desarrollo Científico y TecnológicoCZ.02.1.01/0.0/0.0/15_003/0000466, ANR-15-CE40-0015, 11140566
European Regional Development Fund

    Keywords

    • Mixed-criticality
    • Packing
    • Scheduling

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