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Streaming algorithms for bin packing and vector scheduling

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Cormode, Graham and Veselý, Pavel (2019) Streaming algorithms for bin packing and vector scheduling. In: Workshop on Approximation and Online Algorithms, Munich, Germany, 9-13 Sep 2019. Published in: Approximation and Online Algorithms. WAOA 2019, 11926 pp. 72-88. ISBN 9783030394783. doi:10.1007/978-3-030-39479-0_6

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Official URL: https://doi.org/10.1007/978-3-030-39479-0_6

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Abstract

Problems involving the efficient arrangement of simple objects, as captured by bin packing and makespan scheduling, are fundamental tasks in combinatorial optimization. These are well understood in the traditional online and offline cases, but have been less well-studied when the volume of the input is truly massive, and cannot even be read into memory. This is captured by the streaming model of computation, where the aim is to approximate the cost of the solution in one pass over the data, using small space. As a result, streaming algorithms produce concise input summaries that approximately preserve the optimum value.

We design the first efficient streaming algorithms for these fundamental problems in combinatorial optimization. For Bin Packing, we provide a streaming asymptotic 1+ε -approximation with O˜(1ε) memory, where O˜ hides logarithmic factors. Moreover, such a space bound is essentially optimal. Our algorithm implies a streaming d+ε -approximation for Vector Bin Packing in d dimensions, running in space O˜(dε) . For the related Vector Scheduling problem, we show how to construct an input summary in space O˜(d2⋅m/ε2) that preserves the optimum value up to a factor of 2−1m+ε , where m is the number of identical machines.

Item Type: Conference Item (Paper)
Subjects: Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science > Computer Science
Library of Congress Subject Headings (LCSH): Online algorithms , Combinatorial packing and covering -- Data processing, Computer algorithms, Combinatorial optimization
Series Name: Lecture Notes in Computer Science
Journal or Publication Title: Approximation and Online Algorithms. WAOA 2019
Publisher: Springer
ISBN: 9783030394783
Official Date: 20 July 2019
Dates:
DateEvent
20 July 2019Accepted
Volume: 11926
Page Range: pp. 72-88
DOI: 10.1007/978-3-030-39479-0_6
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
ERC-2014-CoG 647557European Research Councilhttp://dx.doi.org/10.13039/100010663
Conference Paper Type: Paper
Title of Event: Workshop on Approximation and Online Algorithms
Type of Event: Workshop
Location of Event: Munich, Germany
Date(s) of Event: 9-13 Sep 2019
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