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Tight Bounds for Selfish and Greedy Load Balancing

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Abstract

We study the load balancing problem in the context of a set of clients each wishing to run a job on a server selected among a subset of permissible servers for the particular client. We consider two different scenarios. In selfish load balancing, each client is selfish in the sense that it chooses, among its permissible servers, to run its job on the server having the smallest latency given the assignments of the jobs of other clients to servers. In online load balancing, clients appear online and, when a client appears, it has to make an irrevocable decision and assign its job to one of its permissible servers. Here, we assume that the clients aim to optimize some global criterion but in an online fashion. A natural local optimization criterion that can be used by each client when making its decision is to assign its job to that server that gives the minimum increase of the global objective. This gives rise to greedy online solutions. The aim of this paper is to determine how much the quality of load balancing is affected by selfishness and greediness.

We characterize almost completely the impact of selfishness and greediness in load balancing by presenting new and improved, tight or almost tight bounds on the price of anarchy of selfish load balancing as well as on the competitiveness of the greedy algorithm for online load balancing when the objective is to minimize the total latency of all clients on servers with linear latency functions. In addition, we prove a tight upper bound on the price of stability of linear congestion games.

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Authors and Affiliations

  1. Research Academic Computer Technology Institute & Department of Computer Engineering and Informatics, University of Patras, 26500, Rio, Greece

    Ioannis Caragiannis, Christos Kaklamanis & Panagiotis Kanellopoulos

  2. Dipartimento di Informatica, Università di L’Aquila, Via Vetoio, Coppito, 67100, L’Aquila, Italy

    Michele Flammini

  3. Department of Sciences, University of Chieti-Pescara, Viale Pindaro 42, 65127, Pescara, Italy

    Luca Moscardelli

Authors
  1. Ioannis Caragiannis
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  2. Michele Flammini
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  3. Christos Kaklamanis
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  4. Panagiotis Kanellopoulos
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  5. Luca Moscardelli
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Correspondence to Christos Kaklamanis.

Additional information

A preliminary version of the results in this paper appeared in Proceedings of the 33rd International Colloquium on Automata, Languages and Programming (ICALP ’06), LNCS, vol. 4168, pp. 184–195. Springer, Berlin (2006). This work was partially supported by the European Union under IST FET Integrated Project 015964 AEOLUS and COST Action 293 GRAAL, and by a “Caratheodory” basic research grant from the University of Patras.

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Caragiannis, I., Flammini, M., Kaklamanis, C. et al. Tight Bounds for Selfish and Greedy Load Balancing. Algorithmica 61, 606–637 (2011). https://doi.org/10.1007/s00453-010-9427-8

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  • DOI: https://doi.org/10.1007/s00453-010-9427-8

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