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The Online Multicommodity Connected Facility Location Problem

  • Mário César San FeliceEmail author
  • Cristina G. Fernandes
  • Carla Negri Lintzmayer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10787)

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.

Keywords

Online algorithms Competitive analysis Facility Location Steiner Forest Rent-or-buy problems Randomized algorithms 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of ComputingFederal University of São CarlosSão CarlosBrazil
  2. 2.Department of Computer ScienceUniversity of São PauloSão PauloBrazil
  3. 3.Center for Mathematics, Computation and CognitionFederal University of ABCSanto AndréBrazil

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