Dynamic pricing of servers on trees

Ilan Reuven Cohen; Alon Eden; Amos Fiat; Łukasz Jeż

doi:10.4230/LIPIcs.APPROX-RANDOM.2019.10

Dynamic pricing of servers on trees

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

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 [9], 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 α-competitive dynamic pricing scheme exists on the tree if and only if there exists α-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.

Original language	English
Title of host publication	Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019
Editors	Dimitris Achlioptas, Laszlo A. Vegh
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959771252
DOIs	https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.10
State	Published - Sep 2019
Externally published	Yes
Event	22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019 - Cambridge, United States Duration: 20 Sep 2019 → 22 Sep 2019

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	145
ISSN (Print)	1868-8969

Conference

Conference	22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019
Country/Territory	United States
City	Cambridge
Period	20/09/19 → 22/09/19

Bibliographical note

Publisher Copyright:
© Ilan Reuven Cohen, Alon Eden, Amos Fiat, and Łukasz Jeż.

Funding

Funding Ilan Reuven Cohen: Partially supported by the ERC consolidator grant 617951. Alon Eden: Partially supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement number 337122, by the Israel Science Foundation (grant numbers 317/17 and 1841/14). Amos Fiat: Partially supported by the Israel Science Foundation (grant number 1841/14). Łukasz Jeż: Partially supported by Polish National Science Centre grant 2016/22/E/ST6/00499.

Funders	Funder number
Seventh Framework Programme	337122
European Commission	617951
Israel Science Foundation	1841/14, 317/17
Narodowe Centrum Nauki	2016/22/E/ST6/00499
Seventh Framework Programme

Keywords

K-server problem
Online algorithms
Online mechanisms
Online pricing

Access to Document

10.4230/LIPIcs.APPROX-RANDOM.2019.10

Cite this

Cohen, I. R., Eden, A., Fiat, A., & Jeż, Ł. (2019). Dynamic pricing of servers on trees. In D. Achlioptas, & L. A. Vegh (Eds.), Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019 Article 10 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 145). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.10

Cohen, Ilan Reuven ; Eden, Alon ; Fiat, Amos et al. / Dynamic pricing of servers on trees. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019. editor / Dimitris Achlioptas ; Laszlo A. Vegh. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. (Leibniz International Proceedings in Informatics, LIPIcs).

@inproceedings{fb79fe352a4947e0a955d675ab2731e3,

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abstract = "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 [9], 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 α-competitive dynamic pricing scheme exists on the tree if and only if there exists α-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.",

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Cohen, IR, Eden, A, Fiat, A & Jeż, Ł 2019, Dynamic pricing of servers on trees. in D Achlioptas & LA Vegh (eds), Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019., 10, Leibniz International Proceedings in Informatics, LIPIcs, vol. 145, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019, Cambridge, United States, 20/09/19. https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.10

Dynamic pricing of servers on trees. / Cohen, Ilan Reuven; Eden, Alon; Fiat, Amos et al.
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019. ed. / Dimitris Achlioptas; Laszlo A. Vegh. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. 10 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 145).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Jeż, Łukasz

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N2 - 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 [9], 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 α-competitive dynamic pricing scheme exists on the tree if and only if there exists α-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.

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Cohen IR, Eden A, Fiat A, Jeż Ł. Dynamic pricing of servers on trees. In Achlioptas D, Vegh LA, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2019. 10. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.APPROX-RANDOM.2019.10

Dynamic pricing of servers on trees

Abstract

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Bibliographical note

Funding

Keywords

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