NDLI: Packing small vectors

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Locally adaptive optimization: adaptive seeding for monotone submodular functions

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Simple and fast rounding algorithms for directed and node-weighted multiway cut

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Maximum matchings in dynamic graph streams and the simultaneous communication model

Incidence geometries and the pass complexity of semi-streaming set cover

Clustering problems on sliding windows

Gowers norm, function limits, and parameter estimation

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Approximately efficient double auctions with strong budget balance

Interpolating between truthful and non-truthful mechanisms for combinatorial auctions

On the complexity of dynamic mechanism design

Simple pricing schemes for consumers with evolving values

On approximating strip packing with a better ratio than 3/2

Packing small vectors

Approximation schemes for machine scheduling with resource (in-)dependent processing times

Integrality gaps and approximation algorithms for dispersers and bipartite expanders

Improved approximation for vector bin packing

Connectivity in bridge-addable graph classes: the mcdiarmid-steger-welsh conjecture

Recovery and rigidity in a regular stochastic block model

Distance in the forest fire model how far are you from eve?

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Constructive algorithm for path-width of matroids

Approximation of non-boolean 2CSP

An FPTAS for minimizing indefinite quadratic forms over integers in polyhedra

Nearly optimal NP-hardness of unique coverage

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Discrete gaussian sampling reduces to CVP and SVP

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Obstructions for three-coloring graphs with one forbidden induced subgraph

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An improved bound on the fraction of correctable deletions

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Sampling on lattices with free boundary conditions using randomized extensions

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Partial resampling to approximate covering integer programs

Algorithmic and enumerative aspects of the moser-tardos distribution

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Packing small vectors

Content Provider	ACM Digital Library
Author	Roytman, Alan Azar, Yossi Cohen, Ilan Reuven Fiat, Amos
Abstract	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(log d)-competitive algorithm was known. We improve this to a constant competitive ratio, arbitrarily close to ε ≈ 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.
Starting Page	1511
Ending Page	1525
Page Count	15
File Format	PDF
ISBN	9781611974331
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2016-01-10
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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