TY - GEN

T1 - Tight bounds for online vector bin packing

AU - Azar, Yossi

AU - Cohen, Ilan

AU - Kamara, Seny

AU - Shepherd, Bruce

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Bin packing

KW - Competitive ratio

KW - Graph-colouring

KW - Lower bounds

KW - Online algorithms

KW - Vector packing

UR - http://www.scopus.com/inward/record.url?scp=84879829456&partnerID=8YFLogxK

U2 - 10.1145/2488608.2488730

DO - 10.1145/2488608.2488730

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AN - SCOPUS:84879829456

SN - 9781450320290

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 961

EP - 970

BT - STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing

T2 - 45th Annual ACM Symposium on Theory of Computing, STOC 2013

Y2 - 1 June 2013 through 4 June 2013

ER -