Online Bin Covering with Limited Migration

Authors Sebastian Berndt, Leah Epstein, Klaus Jansen, Asaf Levin, Marten Maack, Lars Rohwedder

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Author Details

Sebastian Berndt
  • Department of Computer Science, Kiel University, Kiel, Germany
Leah Epstein
  • Department of Mathematics, University of Haifa, Haifa, Israel
Klaus Jansen
  • Department of Computer Science, Kiel University, Kiel, Germany
Asaf Levin
  • Faculty of Industrial Engineering and Management, The Technion, Haifa, Israel
Marten Maack
  • Department of Computer Science, Kiel University, Kiel, Germany
Lars Rohwedder
  • Department of Computer Science, Kiel University, Kiel, Germany


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".

Cite AsGet BibTex

Sebastian Berndt, Leah Epstein, Klaus Jansen, Asaf Levin, Marten Maack, and Lars Rohwedder. Online Bin Covering with Limited Migration. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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 beta: When an object o of size s(o) arrives, the decisions for objects of total size at most beta * s(o) may be revoked. Usually beta 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 epsilon). We therefore resolve the competitiveness of the bin covering problem with migration.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • online algorithms
  • dynamic algorithms
  • competitive ratio
  • bin covering
  • migration factor


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