Abstract
In the online and incremental variants of Facility Location, the demands arrive one-by-one and must be assigned to an open facility upon arrival, without any knowledge about future demands. In the online variant, the decisions of opening a facility at a particular location and of assigning a demand to some facility are irrevocable. In the incremental variant, the algorithm can also merge existing facilities (and the corresponding demand clusters) with each other, and only the decision of assigning some demands to the same facility is irrevocable. The goal is to maintain, either online or incrementally, a set of facilities and an assignment of the demands to them that minimize the total facility opening cost plus the assignment cost for all demands.
In this survey, we discuss the previous work on online and incremental algorithms for Facility Location. In addition to the main results, namely that the competitive ratio for the online variant is Θ(log nlog log n), where n is the number of demands, and that the competitive ratio for the incremental variant is O(1), we discuss all known online and incremental Facility Location algorithms, sketch the intuition behind them and the main ideas of their competitive analysis, and discuss some applications.
- N. Alon, B. Awerbuch, Y. Azar, N. Buchbinder, and J. Naor. A General Approach to Online Network Optimization Problems. ACM Transactions on Algorithms, 2(4):640--660, 2006. Google ScholarDigital Library
- N. Alon, B. Awerbuch, Y. Azar, N. Buchbinder, and J. Naor. The Online Set Cover Problem. SIAM J. on Computing, 39(2):361--370, 2009. Google ScholarDigital Library
- A. Anagnostopoulos, R. Bent, E. Upfal, and P. Van Hentenryck. A Simple and Deterministic Competitive Algorithm for Online Facility Location. Information and Computation, 194:175--202, 2004. Google ScholarDigital Library
- B.M. Anthony and A. Gupta. Infrastructure Leasing Problems. In Proc. of the 12th Conference on Integer Programming and Combinatorial Optimization (IPCO '07), volume 4513 of LNCS, pages 424--438, 2007. Google ScholarDigital Library
- V. Arya, N. Garg, R. Khandekar, A. Meyerson, K. Munagala, and V. Pandit. Local Search Heuristics for k-Median and Facility Location Problems. SIAM J. on Computing, 33(3):544--562, 2004. Google ScholarDigital Library
- A. Borodin and R. El-Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, 1998. Google ScholarDigital Library
- J. Byrka and K. Aardal. An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem. SIAM J. on Computing, 39(6):2212--2231, 2010. Google ScholarDigital Library
- M. Charikar, C. Chekuri, T. Feder, and R. Motwani. Incremental Clustering and Dynamic Information Retrieval. In Proc. of the 29th ACM Symposium on Theory of Computing (STOC '97), pages 626--635, 1997. Google ScholarDigital Library
- M. Charikar and S. Guha. Improved Combinatorial Algorithms for Facility Location Problems. SIAM J. on Computing, 34(4):803--824, 2005. Google ScholarDigital Library
- M. Charikar, L. O'Callaghan, and R. Panigrahy. Better Streaming Algorithms for Clustering Problems. In Proc. of the 35th ACM Symposium on Theory of Computing (STOC '03), pages 30--39, 2003. Google ScholarDigital Library
- M. Charikar and R. Panigrahy. Clustering to Minimize the Sum of Cluster Diameters. In Proc. of the 33rd ACM Symposium on Theory of Computing (STOC '01), pages 1--10, 2001. Google ScholarDigital Library
- M. Chrobak and C. Kenyon-Mathieu. Online Algorithms Column 10: Competitiveness via Doubling. SIGACT News, 37(4):115--126, 2006. Google ScholarDigital Library
- G. Divéki and C. Imreh. Online Facility Location with Facility Movements. Central European Journal of Operations Research, 2010.Google Scholar
- Z. Drezner and H.W. Hamacher (Editors). Facility Location: Applications and Theory. Springer, 2004.Google Scholar
- J. Fakcharoenphol, S. Rao, and K. Talwar. Approximating Metric Spaces by Tree Metrics. Encyclopedia of Algorithms, pages 51--53, 2008.Google ScholarCross Ref
- D. Fotakis. Incremental Algorithms for Facility Location and k-Median. Theoretical Computer Science, 361(2-3):275--313, 2006. Google ScholarDigital Library
- D. Fotakis. Memoryless Facility Location in One Pass. In Proc. of the 23st Symposium on Theoretical Aspects of Computer Science (STACS '06), volume 3884 of LNCS, pages 608--620, 2006. Google ScholarDigital Library
- D. Fotakis. A Primal-Dual Algorithm for Online Non-Uniform Facility Location. Journal of Discrete Algorithms, 5(1):141--148, 2007. Google ScholarDigital Library
- D. Fotakis. On the Competitive Ratio for Online Facility Location. Algorithmica, 50(1):1--57, 2008. Google ScholarDigital Library
- D. Fotakis and C. Tzamos. Winner-Imposing Strategyproof Mechanisms for Multiple Facility Location Games. In Proc. of the 6th Workshop on Internet and Network Economics (WINE '10), volume 6484 of LNCS, pages 234--245, 2010. Google ScholarDigital Library
- G. Frahling and C. Sohler. Coresets in Dynamic Geometric Data Streams. In Proc. of the 37th ACM Symposium on Theory of Computing (STOC '05), pages 209--217, 2005. Google ScholarDigital Library
- S. Guha and S. Khuller. Greedy Strikes Back: Improved Facility Location Algorithms. Journal of Algorithms, 31(1):228--248, 1999. Google ScholarDigital Library
- S. Guha, A. Meyerson, N. Mishra, R. Motwani, and L. O'Callaghan. Clustering Data Streams: Theory and Practice. IEEE Transactions on Knowledge and Data Engineering, 15(3):515--528, 2003. Google ScholarDigital Library
- S. Guha, N. Mishra, R. Motwani, and L. O'Callaghan. Clustering Data Streams. In Proc. of the 41st IEEE Symposium on Foundations of Computer Science (FOCS '00), pages 359--366, 2000. Google ScholarDigital Library
- P. Indyk. Algorithms for Dynamic Geometric Problems over Data Streams. In Proc. of the 36th ACM Symposium on Theory of Computing (STOC '04), pages 373--380, 2004. Google ScholarDigital Library
- K. Jain, M. Mahdian, E. Markakis, A. Saberi, and V. Vazirani. Greedy Facility Location Algorithms Analyzed Using Dual Fitting with Factor-Revealing LP. J. of the Association for Computing Machinery, 50(6):795--824, 2003. Google ScholarDigital Library
- K. Jain and V. Vazirani. Approximation Algorithms for Metric Facility Location and k-Median Problems Using the Primal-Dual Schema and Lagrangian Relaxation. J. of the Association for Computing Machinery, 48(2):274--296, 2001. Google ScholarDigital Library
- C. Lammersen and C. Sohler. Facility Location in Dynamic Geometric Data Streams. In Proc. of the 16th European Symposium on Algorithms (ESA '08), volume 5193 of LNCS, pages 660--671, 2008. Google ScholarDigital Library
- P. Lu, X. Sun, Y.Wang, and Z.A. Zhu. Asymptotically Optimal Strategy-Proof Mechanisms for Two-Facility Games. In Proc. of the 11th ACM Conference on Electronic Commerce (EC '10), pages 315--324, 2010. Google ScholarDigital Library
- P. Lu, Y.Wang, and Y. Zhou. Tighter Bounds for Facility Games. In Proc. of the 5th Workshop on Internet and Network Economics (WINE '09), volume 5929 of LNCS, pages 137--148, 2009. Google ScholarDigital Library
- M. Mahdian, Y. Ye, and J. Zhang. Improved Approximation Algorithms for Metric Facility Location Problems. In Proc. of the 5th Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX '02), volume 2462 of LNCS, pages 229--242, 2002. Google ScholarDigital Library
- R.R. Mettu and C.G. Plaxton. The Online Median Problem. SIAM J. on Computing, 32(3):816--832, 2003. Google ScholarDigital Library
- A. Meyerson. Online Facility Location. In Proc. of the 42nd IEEE Symposium on Foundations of Computer Science (FOCS '01), pages 426--431, 2001. Google ScholarDigital Library
- A. Meyerson. The Parking Permit Problem. In Proc. of the 46th IEEE Symposium on Foundations of Computer Science (FOCS '05), pages 274--284, 2005. Google ScholarDigital Library
- C. Nagarajan and D.P. Williamson. Offine and Online Facility Leasing. In Proc. of the 13th Conference on Integer Programming and Combinatorial Optimization (IPCO '08), volume 5035 of LNCS, pages 303--315, 2008. Google ScholarDigital Library
- R.L. Francis (Editors) P.B. Mirchandani. Discrete Location Theory. Willey, 1990.Google Scholar
- A.D. Procaccia and M. Tennenholtz. Approximate Mechanism Design Without Money. In Proc. of the 10th ACM Conference on Electronic Commerce (EC '09), pages 177--186, 2009. Google ScholarDigital Library
- J. Schummer and R.V. Vohra. Strategyproof Location on a Network. Journal of Economic Theory, 104:405--428, 2002.Google ScholarCross Ref
- D. Shmoys. Approximation Algorithms for Facility Location Problems. In Proc. of the 3rd Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX '00), volume 1913 of LNCS, pages 27--33, 2000. Google ScholarDigital Library
- D. Shmoys, E. Tardos, and K. Aardal. Approximation Algorithms for Facility Location Problems. In Proc. of the 29th ACM Symposium on Theory of Computing (STOC '97), pages 265--274, 1997. Google ScholarDigital Library
- M. Sviridenko. An Improved Approximation Algorithm for the Metric Uncapacitated Facility Location Problem. In Proc. of the 9th Conference on Integer Programming and Combinatorial Optimization (IPCO '02), volume 2337 of LNCS, pages 240--257, 2002. Google ScholarDigital Library
- M. Thorup. Quick k-Median, k-Center, and Facility Location for Sparse Graphs. SIAM J. on Computing, 34(2):405--432, 2005. Google ScholarDigital Library
Index Terms
- Online and incremental algorithms for facility location
Recommendations
Online Facility Location with Mobile Facilities
SPAA '18: Proceedings of the 30th on Symposium on Parallelism in Algorithms and ArchitecturesWe examine the Online Facility Location Problem in an augmented version, where the online algorithm is allowed to adapt the position of the facilities for costs proportional to the distance by which the position is changed. In this setting, it is ...
Incremental Facility Location Problem and Its Competitive Algorithms
We consider the incremental version of the k -Facility Location Problem, which is a common generalization of the facility location and the k -median problems. The objective is to produce an incremental sequence of facility sets F 1 F 2 F n ,...
Comments