Abstract
Semi-online models where decisions may be revoked in a limited way have been studied extensively in the last years. This is motivated by the fact that the pure online model is often too restrictive to model real-world applications, where some changes might be allowed. A well-studied measure of the amount of decisions that can be revoked is the migration factor β: When an object o of size s(o) arrives, the decisions for objects of total size at most β · s(o) may be revoked. Usually β should be a constant. This means that a small object only leads to small changes. This measure has been successfully investigated for different, classical problems such as bin packing or makespan minimization. The dual of makespan minimization – the Santa Claus or machine covering problem – has also been studied, whereas the dual of bin packing – the bin covering problem – has not been looked at from such a perspective. In this work, we extensively study the bin covering problem with migration in different scenarios. We develop algorithms both for the static case – where only insertions are allowed – and for the dynamic case, where items may also depart. We also develop lower bounds for these scenarios both for amortized migration and for worst-case migration showing that our algorithms have nearly optimal migration factor and asymptotic competitive ratio (up to an arbitrary small ε). We therefore resolve the competitiveness of the bin covering problem with migration.
Original language | English |
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Title of host publication | 27th Annual European Symposium on Algorithms, ESA 2019 |
Editors | Michael A. Bender, Ola Svensson, Grzegorz Herman |
Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
Pages | 18:1–18:14 |
ISBN (Electronic) | 9783959771245 |
DOIs | |
State | Published - Sep 2019 |
Event | 27th Annual European Symposium on Algorithms, ESA 2019 - Munich/Garching, Germany Duration: 9 Sep 2019 → 11 Sep 2019 |
Publication series
Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 144 |
ISSN (Print) | 1868-8969 |
Conference
Conference | 27th Annual European Symposium on Algorithms, ESA 2019 |
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Country/Territory | Germany |
City | Munich/Garching |
Period | 9/09/19 → 11/09/19 |
Bibliographical note
Funding Information:Acknowledgements This work was partially supported by the DFG Project, “Robuste Online-Algorithmen für Scheduling-und Packungsprobleme”, JA 612 /19-1, and by GIF-Project “Polynomial Migration for Online Scheduling”.
Publisher Copyright:
© Sebastian Berndt, Leah Epstein, Klaus Jansen, Asaf Levin, Marten Maack, and Lars Rohwedder.
Keywords
- Bin covering
- Competitive ratio
- Dynamic algorithms
- Migration factor
- Online algorithms
ASJC Scopus subject areas
- Software