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The Online Multicommodity Connected Facility Location Problem

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Approximation and Online Algorithms (WAOA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10787))

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Abstract

Grandoni and Rothvoß introduced the Multicommodity Connected Facility Location problem, a generalization of the Connected Facility Location problem which arises from a combination of the Facility Location and the Steiner Forest problems through the rent-or-buy model. We consider the online version of this problem and present a randomized algorithm that is \(\mathrm {O}(\log ^2 n)\)-competitive, where n is the number of given client pairs. Our algorithm combines the sample-and-augment framework of Gupta, Kumar, Pál, and Roughgarden with previous algorithms for the Online Prize-Collecting Facility Location and the Online Steiner Forest problems. Also, for the special case of the problem with edge scale factor equals 1, we show that a variant of our algorithm is deterministic and \(\mathrm {O}(\log n)\)-competitive. Finally, we speculate on the possibility of finding a \(\mathrm {O}(\log n)\)-competitive algorithm for the general case and the difficulties to achieve such ratio.

M. C. San Felice—Partial support CAPES PNPD 1522390, CNPq 456792/2014-7, FAPESP 2013/03447-6, and FAPESP 2017/11382-2.

C. G. Fernandes—Partial support CNPq 308116/2016-0, 456792/2014-7, and FAPESP 2013/03447-6.

C. N. Lintzmayer—Supported by FAPESP 2016/14132-4.

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Author information

Authors and Affiliations

  1. Department of Computing, Federal University of São Carlos, São Carlos, Brazil

    Mário César San Felice

  2. Department of Computer Science, University of São Paulo, São Paulo, Brazil

    Cristina G. Fernandes

  3. Center for Mathematics, Computation and Cognition, Federal University of ABC, Santo André, Brazil

    Carla Negri Lintzmayer

Authors
  1. Mário César San Felice
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  2. Cristina G. Fernandes
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  3. Carla Negri Lintzmayer
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Corresponding author

Correspondence to Mário César San Felice .

Editor information

Editors and Affiliations

  1. The University of Western Ontario, London, Ontario, Canada

    Roberto Solis-Oba

  2. German University of Technology in Oman, Muscat, Oman

    Rudolf Fleischer

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San Felice, M.C., Fernandes, C.G., Lintzmayer, C.N. (2018). The Online Multicommodity Connected Facility Location Problem. In: Solis-Oba, R., Fleischer, R. (eds) Approximation and Online Algorithms. WAOA 2017. Lecture Notes in Computer Science(), vol 10787. Springer, Cham. https://doi.org/10.1007/978-3-319-89441-6_10

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  • DOI: https://doi.org/10.1007/978-3-319-89441-6_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-89440-9

  • Online ISBN: 978-3-319-89441-6

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