The convergence time for selfish bin packing

G. Dósa, Leah Epstein

Research output: Contribution to journalArticle

7 Citations (Scopus)

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 '), improving the previous bound of Han et al., who showed an upper bound of O(n).

Original languageEnglish
Pages (from-to)37-48
Number of pages12
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8768
Publication statusPublished - 2014

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Bin Packing
Convergence Time
Bins
Costs
Packing
Terminate
Nash Equilibrium
Partition
Valid
Game
Upper bound
Controller
Subset
Arbitrary
Controllers

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

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