Article

Solving fractional packing problems in O^ast(1/ε) iterations

Authors:

G. IyengarAuthors Info & Claims

STOC '04: Proceedings of the thirty-sixth annual ACM symposium on Theory of computing

Pages 146 - 155

https://doi.org/10.1145/1007352.1007382

Published: 13 June 2004 Publication History

Abstract

We adapt a method proposed by Nesterov [16] to design an algorithm that computes ε-optimal solutions to fractional packing problems by solving O^*(ε^-1 √Kn) separable convex quadratic programs, where K is the maximum number of non-zeros per row and n is the number of variables. We also show that the quadratic program can be approximated to any degree of accuracy by an appropriately defined piecewise-linear program. For the special case of the maximum concurrent flow problem on a graph G =(V,E) with rational capacities and demands we obtain an algorithm that computes an Ε-optimal flow by solving O*(ε^-1 K^3/2|E| √|V| (log 1/ε+ L_U + L_D)) shortest path problems, where K is the number of commodities, and L_U, L_D are, respectively, the number of bits needed to store the capacities and demands. We also show that the complexity of computing a maximum multicommodity flow is O^*(1/εlog2(1/ε)). In contrast, previous algorithms required Ω(ε^-2) iterations.

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Cited By

Ahn KGuha S(2018)Access to Data and Number of IterationsACM Transactions on Parallel Computing10.1145/31548554:4(1-40)Online publication date: 3-Jan-2018
https://dl.acm.org/doi/10.1145/3154855
Ahn KGuha SBlelloch GAgrawal K(2015)Access to Data and Number of IterationsProceedings of the 27th ACM symposium on Parallelism in Algorithms and Architectures10.1145/2755573.2755586(202-211)Online publication date: 13-Jun-2015
https://dl.acm.org/doi/10.1145/2755573.2755586
Koufogiannakis CYoung N(2014)A Nearly Linear-Time PTAS for Explicit Fractional Packing and Covering Linear ProgramsAlgorithmica10.1007/s00453-013-9771-670:4(648-674)Online publication date: 1-Dec-2014
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Index Terms

Solving fractional packing problems in O^ast(1/ε) iterations
1. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

STOC '04: Proceedings of the thirty-sixth annual ACM symposium on Theory of computing

June 2004

660 pages

ISBN:1581138520

DOI:10.1145/1007352

Program Chair:
László Babai
University of Chicago, Chicago, IL

Copyright © 2004 ACM.

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Published: 13 June 2004

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Cited By

Ahn KGuha S(2018)Access to Data and Number of IterationsACM Transactions on Parallel Computing10.1145/31548554:4(1-40)Online publication date: 3-Jan-2018
https://dl.acm.org/doi/10.1145/3154855
Ahn KGuha SBlelloch GAgrawal K(2015)Access to Data and Number of IterationsProceedings of the 27th ACM symposium on Parallelism in Algorithms and Architectures10.1145/2755573.2755586(202-211)Online publication date: 13-Jun-2015
https://dl.acm.org/doi/10.1145/2755573.2755586
Koufogiannakis CYoung N(2014)A Nearly Linear-Time PTAS for Explicit Fractional Packing and Covering Linear ProgramsAlgorithmica10.1007/s00453-013-9771-670:4(648-674)Online publication date: 1-Dec-2014
https://dl.acm.org/doi/10.1007/s00453-013-9771-6
Lee YRao SSrivastava NBoneh DRoughgarden TFeigenbaum J(2013)A new approach to computing maximum flows using electrical flowsProceedings of the forty-fifth annual ACM symposium on Theory of Computing10.1145/2488608.2488704(755-764)Online publication date: 1-Jun-2013
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Lee YSidford A(2013)Efficient Accelerated Coordinate Descent Methods and Faster Algorithms for Solving Linear SystemsProceedings of the 2013 IEEE 54th Annual Symposium on Foundations of Computer Science10.1109/FOCS.2013.24(147-156)Online publication date: 26-Oct-2013
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Madry AMitzenmacher MSchulman L(2010)Faster approximation schemes for fractional multicommodity flow problems via dynamic graph algorithmsProceedings of the forty-second ACM symposium on Theory of computing10.1145/1806689.1806708(121-130)Online publication date: 5-Jun-2010
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Iyengar GPhillips DStein C(2010)Feasible and accurate algorithms for covering semidefinite programsProceedings of the 12th Scandinavian conference on Algorithm Theory10.1007/978-3-642-13731-0_15(150-162)Online publication date: 21-Jun-2010
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Saad MTerlaky TVannelli AZhang H(2008)Packing trees in communication networksJournal of Combinatorial Optimization10.1007/s10878-008-9150-416:4(402-423)Online publication date: 4-Apr-2008
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Diedrich FJansen K(2007)An approximation algorithm for the general mixed packing and covering problemProceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies10.5555/2399256.2399268(128-139)Online publication date: 7-Apr-2007
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Chudak FNagano KGabow H(2007)Efficient solutions to relaxations of combinatorial problems with submodular penalties via the Lovász extension and non-smooth convex optimizationProceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms10.5555/1283383.1283393(79-88)Online publication date: 7-Jan-2007
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