Packing small vectors

Yossi Azar, Ilan Reuven Cohen, Amos Fiat, Alan Roytman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Online d-dimensional vector packing models many settings such as minimizing resources in data centers where jobs have multiple resource requirements (CPU, Memory, etc.). However, no online d-dimensional vector packing algorithm can achieve a competitive ratio better than d. Fortunately, in many natural applications, vectors are relatively small, and thus the lower bound does not hold. For sufficiently small vectors, an O(logd)-competitive algorithm was known. We improve this to a constant competitive ratio, arbitrarily close to e ≈ 2.718, given that vectors are sufficiently small. We give improved results for the two dimensional case. For arbitrarily small vectors, the First Fit algorithm for two dimensional vector packing is no better than 2-competitive. We present a natural family of First Fit variants and for optimized parameters get a competitive ratio ≈ 1.48 for sufficiently small vectors. We improve upon the 1.48 competitive ratio -not via a First Fit variant - and give a competitive ratio arbitrarily close to 4/3 for packing small, two dimensional vectors. We show that no algorithm can achieve better than a 4/3 competitive ratio for two dimensional vectors, even if one allows the algorithm to split vectors among arbitrarily many bins.

Original languageEnglish
Title of host publication27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
EditorsRobert Krauthgamer
PublisherAssociation for Computing Machinery
Number of pages15
ISBN (Electronic)9781510819672
StatePublished - 2016
Event27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 - Arlington, United States
Duration: 10 Jan 201612 Jan 2016

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms


Conference27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
Country/TerritoryUnited States


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