A Randomized O(logn)-Competitive Algorithm for the Online Connected Facility Location Problem
The Connected Facility Location (CFL) is a network design problem that arises from a combination of the Uncapacitated Facility Location (FL) and the Steiner Tree (ST) problems. The Online Connected Facility Location problem (OCFL) is an online version of the CFL. San Felice et al. ( 2014 ) presented...
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| Published in | Algorithmica Vol. 76; no. 4; pp. 1139 - 1157 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.12.2016
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0178-4617 1432-0541 |
| DOI | 10.1007/s00453-016-0115-1 |
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| Abstract | The Connected Facility Location (CFL) is a network design problem that arises from a combination of the Uncapacitated Facility Location (FL) and the Steiner Tree (ST) problems. The Online Connected Facility Location problem (OCFL) is an online version of the CFL. San Felice et al. (
2014
) presented a randomized algorithm for the OCFL and proved that it is
O
(
log
2
n
)
-competitive, where
n
is the number of clients. That algorithm combines the sample-and-augment framework of Gupta, Kumar, Pál, and Roughgarden with previous algorithms for the Online Facility Location (OFL) and the Online Steiner Tree (OST) problems. In this paper we use a more precise analysis to show that the same algorithm is
O
(
log
n
)
-competitive. Since there is a lower bound of
Ω
(
log
n
)
for this problem, our result achieves the best possible competitive ratio, asymptotically. |
|---|---|
| AbstractList | The Connected Facility Location (CFL) is a network design problem that arises from a combination of the Uncapacitated Facility Location (FL) and the Steiner Tree (ST) problems. The Online Connected Facility Location problem (OCFL) is an online version of the CFL. San Felice et al. (2014) presented a randomized algorithm for the OCFL and proved that it is O ( log 2 n ) -competitive, where n is the number of clients. That algorithm combines the sample-and-augment framework of Gupta, Kumar, Pál, and Roughgarden with previous algorithms for the Online Facility Location (OFL) and the Online Steiner Tree (OST) problems. In this paper we use a more precise analysis to show that the same algorithm is O ( log n ) -competitive. Since there is a lower bound of Ω ( log n ) for this problem, our result achieves the best possible competitive ratio, asymptotically. The Connected Facility Location (CFL) is a network design problem that arises from a combination of the Uncapacitated Facility Location (FL) and the Steiner Tree (ST) problems. The Online Connected Facility Location problem (OCFL) is an online version of the CFL. San Felice et al. ( 2014 ) presented a randomized algorithm for the OCFL and proved that it is O ( log 2 n ) -competitive, where n is the number of clients. That algorithm combines the sample-and-augment framework of Gupta, Kumar, Pál, and Roughgarden with previous algorithms for the Online Facility Location (OFL) and the Online Steiner Tree (OST) problems. In this paper we use a more precise analysis to show that the same algorithm is O ( log n ) -competitive. Since there is a lower bound of Ω ( log n ) for this problem, our result achieves the best possible competitive ratio, asymptotically. |
| Author | San Felice, Mário César Williamson, David P. Lee, Orlando |
| Author_xml | – sequence: 1 givenname: Mário César surname: San Felice fullname: San Felice, Mário César email: felice@ic.unicamp.br organization: Institute of Computing, Unicamp – sequence: 2 givenname: David P. surname: Williamson fullname: Williamson, David P. organization: School of Operations Research and Information Engineering, Cornell University – sequence: 3 givenname: Orlando surname: Lee fullname: Lee, Orlando organization: Institute of Computing, Unicamp |
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| Keywords | Online algorithms Approximation algorithms Randomized algorithms Connected facility location Competitive analysis Steiner tree |
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| References | Swamy, C., Kumar, A.: Primal-dual algorithms for connected facility location problems. Algorithmica 40(4), 245–269 (2004) LiSA 1.488 approximation algorithm for the uncapacitated facility location problemInf. Comput.20132224558300096110.1016/j.ic.2012.01.0071281.68236 FotakisDOn the competitive ratio for online facility locationAlgorithmica200850157236615310.1007/s00453-007-9049-y1154.68573 San Felice: M.C., Williamson, D.P., Lee, O.: The online connected facility location problem. In: Latin American Theoretical INformatics, 11th Symposium, LATIN 2014, no. 8392 in Lecture Notes in Computer Science, pp. 574–585. Springer, Berlin, Heidelberg (2014) VaziraniVApproximation Algorithms2003GermanySpringer-Verlag Berlin Heidelberg10.1007/978-3-662-04565-7 FotakisDOnline and incremental algorithms for facility locationSIGACT News20114219713110.1145/1959045.1959065 Gupta, A., Kumar, A., Pál, M., Roughgarden, T.: Approximation via cost sharing: Simpler and better approximation algorithms for network design. J. ACM 54(3) (2007). http://portal.acm.org/citation.cfm?doid=1236457.1236458. Article 11 HasanMKJungHChwaKYApproximation algorithms for connected facility locationJ. Comb. Optim.200816155172241527710.1007/s10878-007-9130-01159.90022 Shmoys, D.B.: Approximation algorithms for facility location problems. In: Approximation Algorithms for Combinatorial Optimization, 3rd International Workshop, APPROX 2000, no. 1913 in Lecture Notes in Computer Science, pp. 27–33. Springer, Berlin, Germany (2000). http://dl.acm.org/citation.cfm?id=646688.703104 WilliamsonDPShmoysDBThe Design of Approximation Algorithms2011New York, NYCambridge University Press10.1017/CBO97805119217351219.90004 MahdianMYeYZhangJApproximation algorithms for metric facility location problemsSIAM J. Comput.200636411432224773410.1137/S00975397034357161151.90590 ImaseMWaxmanBMDynamic Steiner tree problemSIAM J. Discrete Math.199143369384110594310.1137/04040330739.05030 FotakisDA primal-dual algorithm for online non-uniform facility locationJ. Discrete Algorithms200751141148228705310.1016/j.jda.2006.03.0011134.90021 Bartal, Y., Fiat, A., Rabani, Y.: : Competitive Algorithms for Distributed Data Management. J. Comput. Syst. Sci. 51(3), 341–358. doi:10.1006/jcss.1995.1073 ByrkaJAardalKAn optimal bifactor approximation algorithm for the metric facility location problemSIAM J. Comput.20103922122231260789910.1137/0707089011205.90173 Nagarajan, C., Williamson, D.P.: Offline and online facility leasing. Discrete Optim. 10(4), 361–370 (2013). doi:10.1016/j.disopt.2013.10.001. http://www.sciencedirect.com/science/article Umboh, S.: Online network design algorithms via hierarchical decompositions. In: Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (2015). To appear. CoRR, abs/1410.4240 Eisenbrand, F., Grandoni, F., Rothvoß, T., Schäfer, G.: Connected facility location via random facility sampling and core detouring. J. Comput. Syst. Sci. 76(8), 709–726 (2010). http://linkinghub.elsevier.com/retrieve Meyerson, A.: Online facility location. In: Foundations of Computer Science, 42nd IEEE Symposium, FOCS 2001, pp. 426–431 (2001). http://dl.acm.org/citation.cfm?id=874063.875567 JungHHasanMKChwaKYA 6.55 factor primal-dual approximation algorithm for the connected facility location problemJ. Comb. Optim.200918258271255116710.1007/s10878-009-9227-81180.90349 BorodinAEl-YanivROnline Computation and Competitive Analysis1998New York, NYCambridge University Press0931.68015 BuchbinderNNaorJSThe design of competitive online algorithms via a primal-dual approachFound. Trends Theor. Comput. Sci.2009393263250649610.1561/04000000241190.68083 GuptaASrinivasanATardosÉCost-sharing mechanisms for network designAlgorithmica20085098119236615610.1007/s00453-007-9065-y1169.68314 |
| References_xml | – reference: WilliamsonDPShmoysDBThe Design of Approximation Algorithms2011New York, NYCambridge University Press10.1017/CBO97805119217351219.90004 – reference: FotakisDOnline and incremental algorithms for facility locationSIGACT News20114219713110.1145/1959045.1959065 – reference: LiSA 1.488 approximation algorithm for the uncapacitated facility location problemInf. Comput.20132224558300096110.1016/j.ic.2012.01.0071281.68236 – reference: JungHHasanMKChwaKYA 6.55 factor primal-dual approximation algorithm for the connected facility location problemJ. Comb. Optim.200918258271255116710.1007/s10878-009-9227-81180.90349 – reference: Umboh, S.: Online network design algorithms via hierarchical decompositions. In: Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (2015). To appear. CoRR, abs/1410.4240 – reference: Swamy, C., Kumar, A.: Primal-dual algorithms for connected facility location problems. Algorithmica 40(4), 245–269 (2004) – reference: Nagarajan, C., Williamson, D.P.: Offline and online facility leasing. Discrete Optim. 10(4), 361–370 (2013). doi:10.1016/j.disopt.2013.10.001. http://www.sciencedirect.com/science/article/ – reference: ImaseMWaxmanBMDynamic Steiner tree problemSIAM J. Discrete Math.199143369384110594310.1137/04040330739.05030 – reference: Bartal, Y., Fiat, A., Rabani, Y.: : Competitive Algorithms for Distributed Data Management. J. Comput. Syst. Sci. 51(3), 341–358. doi:10.1006/jcss.1995.1073 – reference: HasanMKJungHChwaKYApproximation algorithms for connected facility locationJ. Comb. Optim.200816155172241527710.1007/s10878-007-9130-01159.90022 – reference: San Felice: M.C., Williamson, D.P., Lee, O.: The online connected facility location problem. In: Latin American Theoretical INformatics, 11th Symposium, LATIN 2014, no. 8392 in Lecture Notes in Computer Science, pp. 574–585. Springer, Berlin, Heidelberg (2014) – reference: ByrkaJAardalKAn optimal bifactor approximation algorithm for the metric facility location problemSIAM J. Comput.20103922122231260789910.1137/0707089011205.90173 – reference: Gupta, A., Kumar, A., Pál, M., Roughgarden, T.: Approximation via cost sharing: Simpler and better approximation algorithms for network design. J. ACM 54(3) (2007). http://portal.acm.org/citation.cfm?doid=1236457.1236458. Article 11 – reference: Eisenbrand, F., Grandoni, F., Rothvoß, T., Schäfer, G.: Connected facility location via random facility sampling and core detouring. J. Comput. Syst. Sci. 76(8), 709–726 (2010). http://linkinghub.elsevier.com/retrieve/ – reference: FotakisDA primal-dual algorithm for online non-uniform facility locationJ. Discrete Algorithms200751141148228705310.1016/j.jda.2006.03.0011134.90021 – reference: Meyerson, A.: Online facility location. In: Foundations of Computer Science, 42nd IEEE Symposium, FOCS 2001, pp. 426–431 (2001). http://dl.acm.org/citation.cfm?id=874063.875567 – reference: FotakisDOn the competitive ratio for online facility locationAlgorithmica200850157236615310.1007/s00453-007-9049-y1154.68573 – reference: GuptaASrinivasanATardosÉCost-sharing mechanisms for network designAlgorithmica20085098119236615610.1007/s00453-007-9065-y1169.68314 – reference: BuchbinderNNaorJSThe design of competitive online algorithms via a primal-dual approachFound. Trends Theor. Comput. Sci.2009393263250649610.1561/04000000241190.68083 – reference: Shmoys, D.B.: Approximation algorithms for facility location problems. In: Approximation Algorithms for Combinatorial Optimization, 3rd International Workshop, APPROX 2000, no. 1913 in Lecture Notes in Computer Science, pp. 27–33. Springer, Berlin, Germany (2000). http://dl.acm.org/citation.cfm?id=646688.703104 – reference: MahdianMYeYZhangJApproximation algorithms for metric facility location problemsSIAM J. Comput.200636411432224773410.1137/S00975397034357161151.90590 – reference: BorodinAEl-YanivROnline Computation and Competitive Analysis1998New York, NYCambridge University Press0931.68015 – reference: VaziraniVApproximation Algorithms2003GermanySpringer-Verlag Berlin Heidelberg10.1007/978-3-662-04565-7 |
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| SubjectTerms | Algorithm Analysis and Problem Complexity Algorithms Clients Competition Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematics of Computing Operations research Production planning Randomization Site selection Theory of Computation |
| Title | A Randomized O(logn)-Competitive Algorithm for the Online Connected Facility Location Problem |
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