TY - JOUR
AU - György Dósa
AU - Leah Epstein
PY - 2018/01/01
Y2 - 2021/10/21
TI - The Convergence Time for Selfish Bin Packing
JF - Acta Cybernetica
JA - Acta Cybern
VL - 23
IS - 3
SE - Regular articles
DO - 10.14232/actacyb.23.3.2018.8
UR - https://cyber.bibl.u-szeged.hu/index.php/actcybern/article/view/3980
AB - 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).
ER -