Abstract
In this paper we propose the Online Connected Facility Location problem (OCFL), which is an online version of the Connected Facility Location problem (CFL). The CFL is a combination of the Uncapacitated Facility Location problem (FL) and the Steiner Tree problem (ST). We give a randomized O(log2 n)-competitive algorithm for the OCFL via the sample-and-augment framework of Gupta, Kumar, Pál, and Roughgarden and previous algorithms for Online Facility Location (OFL) and Online Steiner Tree (OST). Also, we show that the same algorithm is a deterministic O(logn)-competitive algorithm for the special case of the OCFL with M = 1, where M is a scale factor for the edge costs.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Shmoys, D.B.: Approximation algorithms for facility location problems. In: Jansen, K., Khuller, S. (eds.) APPROX 2000. LNCS, vol. 1913, pp. 27–32. Springer, Heidelberg (2000)
Mahdian, M., Ye, Y., Zhang, J.: Approximation algorithms for metric facility location problems. SIAM Journal on Computing 36, 411–432 (2006)
Byrka, J., Aardal, K.: An optimal bifactor approximation algorithm for the metric facility location problem. SIAM Journal on Computing 39, 2212–2231 (2010)
Li, S.: A 1.488 approximation algorithm for the uncapacitated facility location problem. Information and Computation 222, 45–58 (2013)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Press Syndicate of the University of Cambridge (1998)
Meyerson, A.: Online facility location. In: Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science, pp. 426–431 (2001)
Fotakis, D.: On the competitive ratio for online facility location. Algorithmica 50, 1–57 (2008)
Fotakis, D.: A primal-dual algorithm for online non-uniform facility location. Journal of Discrete Algorithms 5(1), 141–148 (2007)
Nagarajan, C., Williamson, D.P.: Offline and online facility leasing. In: Lodi, A., Panconesi, A., Rinaldi, G. (eds.) IPCO 2008. LNCS, vol. 5035, pp. 303–315. Springer, Heidelberg (2008)
Fotakis, D.: Online and incremental algorithms for facility location. SIGACT News 42(1), 97–131 (2011)
Vazirani, V.: Approximation Algorithms. Springer (2003)
Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms. Cambridge University Press (2011)
Imase, M., Waxman, B.M.: Dynamic Steiner tree problem. SIAM Journal on Discrete Mathematics 4(3), 369–384 (1991)
Buchbinder, N., Naor, J.S.: The design of competitive online algorithms via a primal-dual approach. Foundations and Trends in Theoretical Computer Science 3, 93–263 (2009)
Gupta, A., Kumar, A., Pál, M., Roughgarden, T.: Approximation via cost sharing: Simpler and better approximation algorithms for network design. Journal of the ACM 54(3), Article 11 (2007)
Gupta, A., Srinivasan, A., Tardos, É.: Cost-sharing mechanisms for network design. Algorithmica 50, 98–119 (2008)
Swamy, C., Kumar, A.: Primal-dual algorithms for connected facility location problems. Algorithmica 40(4), 245–269 (2004)
Hasan, M.K., Jung, H., Chwa, K.Y.: Approximation algorithms for connected facility location. Journal of Combinatorial Optimization 16, 155–172 (2008)
Jung, H., Hasan, M.K., Chwa, K.Y.: A 6.55 factor primal-dual approximation algorithm for the connected facility location problem. Journal of Combinatorial Optimization 18, 258–271 (2009)
Eisenbrand, F., Grandoni, F., Rothvoß, T., Schäfer, G.: Connected facility location via random facility sampling and core detouring. Journal of Computer and System Sciences 76(8), 709–726 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
San Felice, M.C., Williamson, D.P., Lee, O. (2014). The Online Connected Facility Location Problem. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_50
Download citation
DOI: https://doi.org/10.1007/978-3-642-54423-1_50
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-54422-4
Online ISBN: 978-3-642-54423-1
eBook Packages: Computer ScienceComputer Science (R0)