@inproceedings{6b956ef871b44eae8720b6a0049c51c4,

title = "Tight bounds for online vector bin packing",

abstract = "In the d-dimensional bin packing problem (VBP), one is given vectors x 1, x2,..., xn 2 Rd and the goal is to find a partition into a minimum number of feasible sets: {1, 2 :..., n} = ∪s i Bi. A set Bi is feasible if jεBi xj ≤ 1, where 1 denotes the all 1's vector. For online VBP, it has been outstanding for almost 20 years to clarify the gap between the best lower bound Ω(1) on the competitive ratio versus the best upper bound of O(d). We settle this by describing a (d1-ε) lower bound. We also give strong lower bounds (of Ω(d 1/B-ε) ) if the bin size B Z+ is allowed to grow. Finally, we discuss almost-matching upper bound results for general values of B; we show an upper bound whose exponent is additively shifted by 1{"} from the lower bound exponent.",

keywords = "Bin packing, Competitive ratio, Graph-colouring, Lower bounds, Online algorithms, Vector packing",

author = "Yossi Azar and Ilan Cohen and Seny Kamara and Bruce Shepherd",

year = "2013",

doi = "10.1145/2488608.2488730",

language = "אנגלית",

isbn = "9781450320290",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

pages = "961--970",

booktitle = "STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing",

note = "null ; Conference date: 01-06-2013 Through 04-06-2013",

}