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The Convergence Time for Selfish Bin Packing

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Algorithmic Game Theory (SAGT 2014)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 8768))

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Abstract

In classic bin packing, the objective is to partition a set of n items with positive rational sizes in (0,1] into a minimum number of subsets called bins, such that the total size of the items of each bin at most 1. We study a bin packing game where the cost of each bin is 1, and given a valid packing of the items, each item has a cost associated with it, such that the items that are packed into a bin share its cost equally. We find tight bounds on the exact worst-case number of steps in processes of convergence to pure Nash equilibria. Those are processes that are given an arbitrary packing. As long as there exists an item that can reduce its cost by moving from its bin to another bin, in each step, a controller selects such an item and instructs it to perform such a beneficial move. The process terminates when no further beneficial moves exist. The function of n that we find is Θ(n 3/2), improving the previous bound of Han et al., who showed an upper bound of O(n 2).

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Pannonia, Veszprém, Hungary

    György Dósa

  2. Department of Mathematics, University of Haifa, Haifa, Israel

    Leah Epstein

Authors
  1. György Dósa
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  2. Leah Epstein
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Editor information

Editors and Affiliations

  1. Faculty of Industrial Engineering and Management, Technion Israel Institute of Technology, Israel

    Ron Lavi

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Dósa, G., Epstein, L. (2014). The Convergence Time for Selfish Bin Packing. In: Lavi, R. (eds) Algorithmic Game Theory. SAGT 2014. Lecture Notes in Computer Science, vol 8768. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44803-8_4

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  • DOI: https://doi.org/10.1007/978-3-662-44803-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44802-1

  • Online ISBN: 978-3-662-44803-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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