The convergence time for selfish bin packing

G. Dósa, Leah Epstein

Research output: Contribution to journalArticle

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 an initial 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 converges when no further beneficial moves exist. The tight function of n that we find is in Θ(n3/2). This improves the previous bound of Ma et al. [14], who showed an upper bound of O(n2).

Original languageEnglish
Pages (from-to)853-865
Number of pages13
JournalActa Cybernetica
Volume23
Issue number3
DOIs
Publication statusPublished - Jan 1 2018

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software
  • Computer Science (miscellaneous)
  • Computer Vision and Pattern Recognition
  • Management Science and Operations Research
  • Information Systems and Management
  • Electrical and Electronic Engineering

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