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A primal-dual resource augmentation analysis of a constant approximate algorithm for stable coalitions in a cluster

Published: 14 June 2008 Publication History

Abstract

In this paper we study the following Cluster Profit Problem. Highly parallelizable requests are present on some network nodes. Each request is associated with a tuple (g, r). The requester is willing to pay kg if k machines execute the request in parallel. If some machines work on a request, the machines must pay the request processing cost, r, as well as connection costs to the request. The problem is to find a profit maximizing assignment of machines to requests, such that each machine works on at most one request. The Cluster Profit Problem can be viewed as a profit maximizing variant of the Facility Location Problem. We provide and analyze an algorithm under resource augmentation for the Cluster Profit Problem. Resource augmentation is a technique made famous by the LRU caching analysis. We compare our algorithm with the optimal algorithm operating on a network graph that has a constant factor longer distances. We prove our algorithm is a constant approximation under this resource augmentation. We also show that our algorithm is resilient to group deviations if deviating increases communication costs by a constant factor.

References

[1]
A. Borodin and R. El-Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, Cambridge, U.K., 1998.
[2]
M. Charikar, S. Khuller, D. Mount, and G. Narasimhan. Algorithms for facility location problems with outliers. In Proceedings of the 12th annual ACM-SIAM Symposium on Discrete algorithms, pages 642--651, Washington, DC, January 2001.
[3]
B.G. Chun, K. Chaudhuri, H. Wee, M. Barreno, C. Papadimitriou, and J. Kubiatowicz. Selfish caching in distributed systems: a game-theoretic analysis. In Proceedings of the 23rd annual ACM Symposium on Principles of Distributed Computing, pages 21--30, St. John?s, Newfoundland, July 2004.
[4]
Z. Drezner and H. W. Hamacher. Facility Location: applications and theory. Springer, New York, 2002.
[5]
A. Fabrikant, A. Luthra, E. Maneva, C. H. Papadimitriou, and S. Shenker. On a network creation game. In Proceedings of the 22nd annual symposium on Principles of Distributed Computing, pages 347--351, Boston, MA, July 2003.
[6]
M. X. Goemans and M. Skutella. Cooperative facility location games. Journal of Algorithms, 50:194--214, 2004.
[7]
D. S. Hochbaum. Heuristics for the fixed cost median problem. Mathematical Programming, 22:148--162, 1982.
[8]
K. Jain, M. Mahdian, E. Markakis, A. Saberi, and V. V. Vazirani. Greedy facility location algorithms analyzed using dual fitting with factor-revealing lp. J. ACM, 50(6):795--824, 2003.
[9]
K. Jain and V. V. Vazirani. Primal-dual approximation algorithms for metric facility location and k-median problem. In Proceedings of the 40th Annual Symposium on Foundations of Computer Science, page 2, New York City, October 1999.
[10]
Bala Kalyanasundaram and Kirk Pruhs. Speed is as powerful as clairvoyance. J. ACM, 47(4):617--643, 2000.
[11]
L. Kaufman, M.V. Eede, and P. Hansen. A plant and warehouse location problem. Operational Research Quarterly, 28:547--554, 1977.
[12]
I. Keider, R. Melamed, and A. Orda. Equicast: scalable multicast with selfish users. In Proceedings of the 25th annual symposium on Principles of Distributed Computing, pages 63--71, Denver, Colorado, USA, July 2006.
[13]
R. R. Mettu and C. G. Plaxton. The online median problem. SIAM Journal on Computing, 32:816--832, 2003.
[14]
Thomas Moscibroda and Roger Wattenhofer. Facility location: distributed approximation. In Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing, pages 108--117, 2005.
[15]
M. Pál and E. Tardos. Group strategy proof mechanisms via primal-dual algorithms. In Proceedings of the 44th annual IEEE Symposium on Foundations of Computer Science, pages 584--593, October 2003.
[16]
Cynthia A. Phillips, Cliff Stein, Eric Torng, and Joel Wein. Optimal time-critical scheduling via resource augmentation (extended abstract). In STOC?97: Proceedings of the twenty-ninth annual ACM symposium on Theory of computing, pages 140--149, 1997.
[17]
T. Sandholm, K. Larson, M. Andersson, O. Shehory, and F. Tohme. Coalition structure generation with worst case guarantees. Artificial Intelligence, 111:209--238, March 1999.
[18]
O. Shehory and S. Kraus. Task allocation via coalition formation among autonomous agents. International Joint Conference on Artificial Intelligence, 14:655--661, August 1995.
[19]
D. B. Shmoys, E. Tardos, and K. Aardal. Approximation algorithms for facility location problems. In Proceedings of the 29th annual ACM symposium on Theory of Computing, pages 265--274, El. Paso, Texas, USA, July 1997.
[20]
M. Shubik. Game Theory In The Social Sciences. MIT Press, Cambridge, Massachussetts, 1984.
[21]
Daniel D. Sleator and Robert E. Tarjan. Amortized efficiency of list update and paging rules. Commun. ACM, 28(2):202--208, 1985.
[22]
V. V. Vazirani. Approximation Algorithms. Springer, New York, 2001.

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  • (2010)Fast primal-dual distributed algorithms for scheduling and matching problemsDistributed Computing10.1007/s00446-010-0100-x22:4(269-283)Online publication date: 1-May-2010

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  1. A primal-dual resource augmentation analysis of a constant approximate algorithm for stable coalitions in a cluster

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    cover image ACM Conferences
    SPAA '08: Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
    June 2008
    380 pages
    ISBN:9781595939739
    DOI:10.1145/1378533
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    Published: 14 June 2008

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    Author Tags

    1. approximate core equilibrium
    2. facility location
    3. primal-dual
    4. resource augmentation

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    • (2010)Fast primal-dual distributed algorithms for scheduling and matching problemsDistributed Computing10.1007/s00446-010-0100-x22:4(269-283)Online publication date: 1-May-2010

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