Dynamic Pricing of Servers on Trees

Authors Ilan Reuven Cohen, Alon Eden, Amos Fiat, Łukasz Jeż

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Author Details

Ilan Reuven Cohen
  • TU Eindhoven, The Netherlands
  • CWI, Amsterdam, The Netherlands
Alon Eden
  • Tel Aviv University, Israel
Amos Fiat
  • Tel Aviv University, Israel
Łukasz Jeż
  • University of Wrocław, Poland

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Ilan Reuven Cohen, Alon Eden, Amos Fiat, and Łukasz Jeż. Dynamic Pricing of Servers on Trees. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 10:1-10:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


In this paper we consider the k-server problem where events are generated by selfish agents, known as the selfish k-server problem. In this setting, there is a set of k servers located in some metric space. Selfish agents arrive in an online fashion, each has a request located on some point in the metric space, and seeks to serve his request with the server of minimum distance to the request. If agents choose to serve their request with the nearest server, this mimics the greedy algorithm which has an unbounded competitive ratio. We propose an algorithm that associates a surcharge with each server independently of the agent to arrive (and therefore, yields a truthful online mechanism). An agent chooses to serve his request with the server that minimizes the distance to the request plus the associated surcharge to the server. This paper extends [Ilan Reuven Cohen et al., 2015], which gave an optimal k-competitive dynamic pricing scheme for the selfish k-server problem on the line. We give a k-competitive dynamic pricing algorithm for the selfish k-server problem on tree metric spaces, which matches the optimal online (non truthful) algorithm. We show that an alpha-competitive dynamic pricing scheme exists on the tree if and only if there exists alpha-competitive online algorithm on the tree that is lazy and monotone. Given this characterization, the main technical difficulty is coming up with such an online algorithm.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Theory of computation → Algorithmic mechanism design
  • Online algorithms
  • Online mechanisms
  • k-server problem
  • Online pricing


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  1. Baruch Awerbuch, Yossi Azar, and Adam Meyerson. Reducing Truth-telling Online Mechanisms to Online Optimization. In Proceedings of the Thirty-fifth Annual ACM Symposium on Theory of Computing, STOC '03, pages 503-510, New York, NY, USA, 2003. ACM. URL: https://doi.org/10.1145/780542.780616.
  2. Nikhil Bansal, Marek Eliás, Lukasz Jez, Grigorios Koumoutsos, and Kirk Pruhs. Tight Bounds for Double Coverage Against Weak Adversaries. Theory Comput. Syst., 62(2):349-365, 2018. URL: https://doi.org/10.1007/s00224-016-9703-3.
  3. Yair Bartal and Elias Koutsoupias. On the competitive ratio of the work function algorithm for the k-server problem. Theor. Comput. Sci., 324(2-3):337-345, 2004. URL: https://doi.org/10.1016/j.tcs.2004.06.001.
  4. Allan Borodin, Nathan Linial, and Michael E. Saks. An Optimal On-Line Algorithm for Metrical Task System. J. ACM, 39(4):745-763, 1992. URL: https://doi.org/10.1145/146585.146588.
  5. Sébastien Bubeck, Michael B. Cohen, Yin Tat Lee, James R. Lee, and Aleksander Madry. k-server via multiscale entropic regularization. In Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018, Los Angeles, CA, USA, June 25-29, 2018, pages 3-16, 2018. URL: https://doi.org/10.1145/3188745.3188798.
  6. Niv Buchbinder, Liane Lewin-Eytan, Joseph (Seffi) Naor, and Ariel Orda. Non-Cooperative Cost Sharing Games via Subsidies. Theor. Comp. Sys., 47(1):15-37, July 2010. URL: https://doi.org/10.1007/s00224-009-9197-3.
  7. Marek Chrobak, Howard J. Karloff, T. H. Payne, and Sundar Vishwanathan. New Results on Server Problems. SIAM J. Discrete Math., 4(2):172-181, 1991. URL: https://doi.org/10.1137/0404017.
  8. Marek Chrobak and Lawrence L. Larmore. An Optimal On-Line Algorithm for k-Servers on Trees. SIAM J. Comput., 20(1):144-148, 1991. URL: https://doi.org/10.1137/0220008.
  9. Ilan Reuven Cohen, Alon Eden, Amos Fiat, and Lukasz Jez. Pricing Online Decisions: Beyond Auctions. In Piotr Indyk, editor, Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, San Diego, CA, USA, January 4-6, 2015, pages 73-91. SIAM, 2015. URL: https://doi.org/10.1137/1.9781611973730.7.
  10. Alon Eden, Michal Feldman, Amos Fiat, and Tzahi Taub. Truthful Prompt Scheduling for Minimizing Sum of Completion Times. In 26th Annual European Symposium on Algorithms, ESA 2018, August 20-22, 2018, Helsinki, Finland, pages 27:1-27:14, 2018. URL: https://doi.org/10.4230/LIPIcs.ESA.2018.27.
  11. Michal Feldman, Amos Fiat, and Alan Roytman. Makespan Minimization via Posted Prices. In Proceedings of the 2017 ACM Conference on Economics and Computation, EC '17, Cambridge, MA, USA, June 26-30, 2017, pages 405-422, 2017. URL: https://doi.org/10.1145/3033274.3085129.
  12. Amos Fiat, Yishay Mansour, and Uri Nadav. Efficient contention resolution protocols for selfish agents. In Nikhil Bansal, Kirk Pruhs, and Clifford Stein, editors, Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007, New Orleans, Louisiana, USA, January 7-9, 2007, pages 179-188. SIAM, 2007. URL: http://dl.acm.org/citation.cfm?id=1283383.1283403.
  13. Sungjin Im, Benjamin Moseley, Kirk Pruhs, and Clifford Stein. Minimizing Maximum Flow Time on Related Machines via Dynamic Posted Pricing. In Kirk Pruhs and Christian Sohler, editors, 25th Annual European Symposium on Algorithms, ESA 2017, September 4-6, 2017, Vienna, Austria, volume 87 of LIPIcs, pages 51:1-51:10. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.ESA.2017.51.
  14. Sandy Irani and Ronitt Rubinfeld. A Competitive 2-Server Algorithm. Inf. Process. Lett., 39(2):85-91, 1991. URL: https://doi.org/10.1016/0020-0190(91)90160-J.
  15. Bala Kalyanasundaram and Kirk Pruhs. Online Weighted Matching. J. Algorithms, 14(3):478-488, 1993. URL: https://doi.org/10.1006/jagm.1993.1026.
  16. Elias Koutsoupias. The k-server problem. Computer Science Review, 3(2):105-118, 2009. URL: https://doi.org/10.1016/j.cosrev.2009.04.002.
  17. Elias Koutsoupias and Christos H. Papadimitriou. On the k-Server Conjecture. J. ACM, 42(5):971-983, 1995. URL: https://doi.org/10.1145/210118.210128.
  18. Ron Lavi and Noam Nisan. Competitive Analysis of Incentive Compatible On-line Auctions. In Proceedings of the 2Nd ACM Conference on Electronic Commerce, EC '00, pages 233-241, New York, NY, USA, 2000. ACM. URL: https://doi.org/10.1145/352871.352897.
  19. Mark S. Manasse, Lyle A. McGeoch, and Daniel Dominic Sleator. Competitive Algorithms for Server Problems. J. Algorithms, 11(2):208-230, 1990. URL: https://doi.org/10.1016/0196-6774(90)90003-W.
  20. Daniel Dominic Sleator and Robert Endre Tarjan. Amortized Efficiency of List Update and Paging Rules. Commun. ACM, 28(2):202-208, 1985. URL: https://doi.org/10.1145/2786.2793.