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Approximation-Friendly Discrepancy Rounding

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Integer Programming and Combinatorial Optimization (IPCO 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9682))

Abstract

Rounding linear programs using techniques from discrepancy is a recent approach that has been very successful in certain settings. However this method also has some limitations when compared to approaches such as randomized and iterative rounding. We provide an extension of the discrepancy-based rounding algorithm due to Lovett-Meka that (i) combines the advantages of both randomized and iterated rounding, (ii) makes it applicable to settings with more general combinatorial structure such as matroids. As applications of this approach, we obtain new results for various classical problems such as linear system rounding, degree-bounded matroid basis and low congestion routing.

N. Bansal—Supported by a NWO Vidi grant 639.022.211 and an ERC consolidator grant 617951.

V. Nagarajan—Supported in part by a faculty award from Bloomberg Labs.

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Notes

  1. 1.

    The results below generalize to arbitrary real matrices A and vectors x in natural ways, but we consider 0–1 case for simplicity.

  2. 2.

    We thank an anonymous reviewer for pointing this out.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands

    Nikhil Bansal

  2. Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, USA

    Viswanath Nagarajan

Authors
  1. Nikhil Bansal
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  2. Viswanath Nagarajan
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Corresponding author

Correspondence to Viswanath Nagarajan .

Editor information

Editors and Affiliations

  1. Université de Liège, Liège, Belgium

    Quentin Louveaux

  2. Technische Universität Berlin, Berlin, Germany

    Martin Skutella

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Bansal, N., Nagarajan, V. (2016). Approximation-Friendly Discrepancy Rounding. In: Louveaux, Q., Skutella, M. (eds) Integer Programming and Combinatorial Optimization. IPCO 2016. Lecture Notes in Computer Science(), vol 9682. Springer, Cham. https://doi.org/10.1007/978-3-319-33461-5_31

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  • DOI: https://doi.org/10.1007/978-3-319-33461-5_31

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-33461-5

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