Abstract
In a facility location problem (FLP) we are given a set of facilities and a set of clients, each of which is to be served by one facility. The goal is to decide which subset of facilities to open, such that the clients will be served at a minimal cost. In this paper we investigate the FLP in a setting where the cost depends on data known only to the clients. This setting typifies modern distributed systems: peer-to-peer file sharing networks, Grid systems, and wireless sensor networks. All of them need to perform network organization, data placement, collective power management, and other tasks of this kind. We propose a local and efficient algorithm that solves FLP in these settings. The algorithm presented here is extremely scalable, entirely decentralized, requires no routing capabilities, and is resilient to failures and changes in the data throughout its execution.
Similar content being viewed by others
References
Arya, V., Garg, N., Khandekar, R., Munagala, K., Pandit, V.: Local search heuristic for k-median and facility location problems. In: STOC ’01: Proceedings of the thirty-third annual ACM symposium on Theory of computing, pp. 21–29. New York, NY, USA (2001)
Awerbuch, B., Bar-Noy, A., Linial, N., Peleg, D.: Compact distributed data structures for adaptive routing. In: STOC ’89: Proceedings of the twentyfirst annual ACM symposium on Theory of computing, pp. 479–489. New York, NY, USA (1989)
Awerbuch, B., Patt-Shamir, B., Varghese, G.: Self-stabilization by local checking and correction (extended abstract). In: IEEE Symposium on Foundations of Computer Science, pp. 268–277. Los Alamitos, CA, USA (1991)
Balinski., M.: On finding integer solutions to linear programs. Proc. IBM Scientific Computing Symp. on Combinatorial Problems, pp. 225–248 (1966)
Birk, Y., Liss, L., Schuster, A., Wolff, R.: A local algorithm for ad hoc majority voting via charge fusion. In: DISC. (2004)
Charikar, M., Guha, S.: Improved combinatorial algorithms for the facility location and k-median problems. In: IEEE Symposium on Foundations of Computer Science, pp. 378–388 (1999)
Dhillon, I.S., Modha, D.S.: A data-clustering algorithm on distributed memory multiprocessors. In: Large-scale Parallel Data Mining. pp. 245–260 (2002)
Ester, M., Kriegel, H., Sander, J., Wimmer, M., Xu, X.: Incremental clustering for mining in a data warehousing environment. In: VLDB., pp. 323–333 (1998)
Ford, L., Fulkerson, D.: Flows in Networks. Princeton University Press, Princeton, NJ (1962)
Forman, G., Zhang, B.: Distributed data clustering can be efficient and exact. SIGKDD Explor. Newsl. 2(2), 34–38 (2000)
Foti, D., Lipari, D., Pizzuti, C., Talia, D.: Scalable parallel clustering for data mining on multicomputers. In: IPDPS 00: Proceedings of the 15 IPDPS 2000 Workshops on Parallel and Distributed Processing, pp. 390–398. London, UK (2000)
Guha, S., Khuller, S.: Greedy strikes back: improved facility location algorithms. In: SODA: ACM-SIAM Symposium on Discrete Algorithms (A Conference on Theoretical and Experimental Analysis of Discrete Algorithms)(1998)
Gupta, P., Kumar, P.R.: The capacity of wireless networks. IEEE Trans. Inf. Theory 46(2), 388–404 (2000)
Jaffe, J., Moss, F.: A responsive routing algorithm for computer networks. IEEE Trans. Commun. pp. 1758–1762 (1982)
Jain, K., Vazirani, V.V.: Primal–Dual approximation algorithms for metric facility location and k-median problems. In: IEEE Symposium on Foundations of Computer Science. pp. 2–13 (1999)
Kaashoek, F., Karger, D.: Koorde: A simple degree-optimal distributed hash table. Peer-to-Peer Systems II: Second International Workshop (2003)
Kleinberg, J., Papadimitriou, C., Raghavan, P.: A microeconomic view of data mining. Data Mining and Knowledge Discovery 2(4), 311–324 (1998)
Korupolu, M.R., Plaxton, C.G., Rajaraman, R.: Analysis of a local search heuristic for facility location problems. In: SODA: ACM-SIAM Symposium on Discrete Algorithms (A Conference on Theoretical and Experimental Analysis of Discrete Algorithms). pp. 1–10 (1998)
Kuhn, F., Moscibroda, T., Wattenhofer, R.: What cannot be computed locally!. In: PODC 04: Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing. New York, NY, USA, pp. 300–309 (2004)
Kutten, S., Patt-Shamir, B.: Time-adaptive self stabilization. In: PODC 97: Proceedings of the sixteenth annual ACM symposium on Principles of distributed computing. New York, NY, USA, pp. 149–158 (1997)
Kutten, S., Peleg, D.: Fault-local distributed mending (extended abstract). In: PODC 95: Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing. New York, NY, USA, pp. 20–27 (1995)
Linial, N.: Locality in distributed graph algorithms. SIAM Comput. J. 21(1), 193–201 (1992)
Medina, A., Lakhina, A., Matta, I., Byers, J.: BRITE: universal topology generation from a user’s perspective. Technical report, Boston, MA, USA (2001)
Moscibroda, T., Wattenhofer, R.: Facility location: distributed approximation. In: PODC 05: Proceedings of the twenty-fourth annual ACMSIGACT-SIGOPS symposium on Principles of distributed computing. New York, NY, USA, pp. 108–117 (2005)
Naor, M., Stockmeyer, L.: What can be computed locally? In: STOC ’93: Proceedings of the twenty-fifth annual ACM symposium on Theory of computing, pp. 184–193. New York, NY, USA, (1993)
Page, C.: Astrogrid and data mining. In: Starck, J.-L., Murtagh, F.D. (eds.) Proc. SPIE Vol. 4477, pp. 53–60, Astronomical Data Analysis, pp. 53–60 (2001)
Wolff, R., Schuster, A.: Association rule mining in peer-to-peer systems. In: ICDM 03: Proceedings of the Third IEEE International Conference on Data Mining. Washington, DC, USA, pp. 363 (2003)
Wolff, R., Schuster, A.: Association rule mining in peer-to-peer systems. IEEE Trans. Syst. Man Cybern., Part B 34(6), 2426–2438 (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Krivitski, D., Schuster, A. & Wolff, R. A Local Facility Location Algorithm for Large-scale Distributed Systems. J Grid Computing 5, 361–378 (2007). https://doi.org/10.1007/s10723-007-9069-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10723-007-9069-5