SIAM Journal on Computing
An on-line graph coloring algorithm with sublinear performance ratio
Discrete Mathematics
Lower bounds for on-line graph coloring
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
New Bounds for Variable-Sized Online Bin Packing
SIAM Journal on Computing
On-line Packing and Covering Problems
Developments from a June 1996 seminar on Online algorithms: the state of the art
On variable sized vector packing
Acta Cybernetica
On Multidimensional Packing Problems
SIAM Journal on Computing
Adaptivity and approximation for stochastic packing problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
CLOUD '10 Proceedings of the 2010 IEEE 3rd International Conference on Cloud Computing
Online primal-dual algorithms for covering and packing problems
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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In the d-dimensional bin packing problem (VBP), one is given vectors x1,x2, ... ,xn ∈ Rd and the goal is to find a partition into a minimum number of feasible sets: {1,2 ... ,n} = ∪is Bi. A set Bi is feasible if ∑j ∈ Bi 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 Ω(d1-ε) lower bound. We also give strong lower bounds (of Ω(d1/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.