The convergence time for selfish bin packing

Dósa, György and Epstein, Leah: The convergence time for selfish bin packing. Acta cybernetica, (23) 3. pp. 853-866. (2018)

[img] Cikk, tanulmány, mű
actacyb_23_3_2018_08.pdf

Download (354kB)

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(n 3/2 ). This improves the previous bound of Ma et al. [14], who showed an upper bound of O(n 2).

Item Type: Article
Journal or Publication Title: Acta cybernetica
Date: 2018
Volume: 23
Number: 3
Page Range: pp. 853-866
ISSN: 0324-721X
Uncontrolled Keywords: Konvergencia, Matematika
Additional Information: Bibliogr.: p. 864-865. ; Összefoglalás angol nyelven
Date Deposited: 2018. Nov. 08. 08:34
Last Modified: 2018. Nov. 08. 08:34
URI: http://acta.bibl.u-szeged.hu/id/eprint/55681

Actions (login required)

View Item View Item