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The Online Multicommodity Connected Facility Location Problem

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


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.


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

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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  • DOI: 10.1007/978-3-319-89441-6_10
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Correspondence to Mário César San Felice .

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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.

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