ABSTRACT
In this paper we consider neighborhood load balancing in the context of selfish clients. We assume that a network of n processors is given, with m tasks assigned to the processors. The processors may have different speeds and the tasks may have different weights. Every task is controlled by a selfish user. The objective of the user is to allocate his/her task to a processor with minimum load, where the load of a processor is defined as the weight of its tasks divided by its speed.
We investigate a concurrent probabilistic protocol which works in sequential rounds. In each round every task is allowed to query the load of one randomly chosen neighboring processor. If that load is smaller than the load of the task's current processor, the task will migrate to that processor with a suitably chosen probability. Using techniques from spectral graph theory we obtain upper bounds on the expected convergence time towards approximate and exact Nash equilibria that are significantly better than previous results for this protocol. We show results for uniform tasks on non-uniform processors and the general case where the tasks have different weights and the machines have speeds. To the best of our knowledge, these are the first results for this general setting.
- H. Ackermann, S. Fischer, M. Hoefer, and M. Schöngens. Distributed algorithms for qos load balancing. In Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures, SPAA'09, pages 197--203, New York, NY, USA, 2009. ACM. Google ScholarDigital Library
- C. P. J. Adolphs and P. Berenbrink. Improved Bounds for Discrete Diffusive Load Balancing. To appear at IPDPS 2012, 2012.Google Scholar
- B. Awerbuch, Y. Azar, and R. Khandekar. Fast load balancing via bounded best response. In Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms, SODA '08, pages 314--322, Philadelphia, PA, USA, 2008. Society for Industrial and Applied Mathematics. Google ScholarDigital Library
- P. Berenbrink, T. Friedetzky, L. A. Goldberg, P. W. Goldberg, Z. Hu, and R. Martin. Distributed Selfish Load Balancing. SIAM Journal on Computing, 37(4):1163, 2007. Google ScholarDigital Library
- P. Berenbrink, T. Friedetzky, I. Hajirasouliha, and Z. Hu. Convergence to equilibria in distributed, selfish reallocation processes with weighted tasks. In L. Arge, M. Hoffmann, and E. Welzl, editors, Proceedings of the 15th Annual European Symposium on Algorithms (ESA 2007), volume 4698/2007 of Lecture Notes in Computer Science, pages 41--52. Springer, Springer, October 2007. Google ScholarDigital Library
- P. Berenbrink, M. Hoefer, and T. Sauerwald. Distributed selfish load balancing on networks. In Proceedings of 22nd Symposium on Discrete Algorithms (SODA'11), pages 1487--1497, 2011. Google ScholarDigital Library
- J. E. Boillat. Load balancing and Poisson equation in a graph. Concurrency: Practice and Experience, 2(4):289--313, Dec. 1990. Google ScholarDigital Library
- F. R. K. Chung. Spectral graph theory. AMS Bookstore, 1997.Google Scholar
- G. Cybenko. Dynamic load balancing for distributed memory multiprocessors. Journal of Parallel and Distributed Computing, 7(2):279--301, Oct. 1989. Google ScholarDigital Library
- R. Elsässer, B. Monien, and R. Preis. Diffusion Schemes for Load Balancing on Heterogeneous Networks. Theory of Computing Systems, 35(3):305--320, May 2002.Google Scholar
- R. Elsässer, B. Monien, and S. Schamberger. Distributing unit size workload packages in heterogeneous networks. Journal of Graph Algorithms and Applications, 10(1):51--68, 2006.Google ScholarCross Ref
- E. Even-Dar, A. Kesselman, and Y. Mansour. Convergence time to Nash equilibrium in load balancing. ACM Transactions on Algorithms, 3(3):32--es, Aug. 2007. Google ScholarDigital Library
- E. Even-Dar and Y. Mansour. Fast convergence of selfish rerouting. In Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms (SODA'05), pages 772--781, 2005. Google ScholarDigital Library
- R. Feldmann, M. Gairing, T. Lücking, B. Monien, and M. Rode. Nashification and the coordination ratio for a selfish routing game. In J. Baeten, J. Lenstra, J. Parrow, and G. Woeginger, editors, Automata, Languages and Programming, volume 2719 of Lecture Notes in Computer Science, pages 190--190. Springer Berlin / Heidelberg, 2003. Google ScholarDigital Library
- M. Fiedler. Algebraic connectivity of graphs. Czechoslovak Mathematical Journal, 23(2):298--305, 1973.Google ScholarCross Ref
- S. Fischer, P. Mahonen, M. Schongens, and B. Vocking. Load balancing for dynamic spectrum assignment with local information for secondary users. In New Frontiers in Dynamic Spectrum Access Networks, 2008. DySPAN 2008. 3rd IEEE Symposium on, pages 1--9, oct. 2008.Google ScholarCross Ref
- S. Fischer and B. Vöcking. Adaptive routing with stale information. In Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing (PODC'05), pages 276--283, New York, NY, USA, 2005. ACM. Google ScholarDigital Library
- D. Fotakis, A. Kaporis, and P. Spirakis. Atomic congestion games: Fast, myopic and concurrent. Theory of Computing Systems, 47:38--59, 2010. 10.1007/s00224-009-9198-2. Google ScholarDigital Library
- T. Friedrich and T. Sauerwald. Near-perfect load balancing by randomized rounding. In Proceedings of the 41st annual ACM symposium on Symposium on theory of computing - STOC '09, page 121, New York, New York, USA, May 2009. ACM Press. Google ScholarDigital Library
- B. Mohar. Isoperimetric numbers of graphs. Journal of Combinatorial Theory, Series B, 47(3):274--291, Dec. 1989. Google ScholarDigital Library
- B. Mohar. Eigenvalues, diameter, and mean distance in graphs. Graphs and Combinatorics, 7(1):53--64, Mar. 1991.Google ScholarDigital Library
- Mohar, B. The Laplacian Spectrum of Graphs. In Y. Alavi, editor, Graph theory, combinatorics, and applications, volume 2, pages 871--898. Wiley, 1991.Google Scholar
- S. Muthukrishnan, B. Ghosh, and M. Schultz. First- and Second-Order Diffusive Methods for Rapid, Coarse, Distributed Load Balancing. Theory of Computing Systems, 31(4):331--354, July 1998.Google ScholarCross Ref
- Y. Rabani, A. Sinclair, and R. Wanka. Local divergence of Markov chains and the analysis of iterative load-balancing schemes. In Proceedings 39th Annual Symposium on Foundations of Computer Science (FOCS'98), pages 694--703. IEEE Comput. Soc, 1998. Google ScholarDigital Library
- B. Vöcking. Selfish Load Balancing. In N. Nisan, E. Tardos, T. Roughgarden, and V. Vazirani, editors, Algorithmic Game Theory, chapter 20. Cambridge University Press, 2007.Google Scholar
Index Terms
- Distributed selfish load balancing with weights and speeds
Recommendations
Distributed Selfish Load Balancing on Networks
We study distributed load balancing in networks with selfish agents. In the simplest model considered here, there are n identical machines represented by vertices in a network and m > n selfish agents that unilaterally decide to move from one vertex to ...
Distributed Selfish Load Balancing
Suppose that a set of $m$ tasks are to be shared as equally as possible among a set of $n$ resources. A game-theoretic mechanism to find a suitable allocation is to associate each task with a “selfish agent” and require each agent to select a resource, ...
Improved Bounds for Discrete Diffusive Load Balancing
IPDPS '12: Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing SymposiumIn this paper we consider load balancing in a static and discrete setting where a fixed number of indivisible tasks have to be allocated to processors. We assume uniform tasks but the processors may have different speeds. The load of a processor is the ...
Comments