This Article 
 Bibliographic References 
 Add to: 
Replicated Server Placement with QoS Constraints
October 2006 (vol. 17 no. 10)
pp. 1151-1162

Abstract—The network planning problem of placing replicated servers with QoS constraints is considered. Each server site may consist of multiple server types with varying capacities and each site can be placed in any location among those belonging to a given set. Each client can be served by more than one location as long as the round-trip delay of data requests satisfies predetermined upper bounds. Our main focus is to minimize the cost of using the servers and utilizing the link bandwidth, while serving requests according to their delay constraint. This is an NP-hard problem. A pseudopolynomial and a polynomial algorithm that provide guaranteed approximation factors with respect to the optimal for the problem at hand are presented.

[1] R. Krishnan, D. Raz, and Y. Shavitt, “The Cache Location Problem,” IEEE/ACM Trans. Networking, vol. 8, no. 5, pp. 568-582, Oct. 2000.
[2] B. Li, M. Golin, G. Italiano, and X. Deng, “On the Optimal Placement of Web Proxies in the Internet,” Proc. IEEE INFOCOM, vol. 3, pp. 1282-1290, Mar. 1999.
[3] X. Jia, D. Li, X. Hu, and D. Du, “Optimal Placement of Web Proxies for Replicated Web Servers in the Internet,” The Computer J., vol. 44, no. 5, pp. 329-339, 2001.
[4] X. Jia, D. Li, X. Hu, W. Wu, and D. Du, “Placement of Web-Server Proxies with Consideration of Read and Update Operations on the Internet,” The Computer J., vol. 46, no. 4, 2003.
[5] L. Qiu, V. Padmanabhan, and G. Voelker, “On the Placement of Web Server Replicas,” Proc. IEEE INFOCOM, vol. 3, pp. 1587-1596, Apr. 2001.
[6] Y. Chen, R. Katz, and J. Kubiatowicz, “Dynamic Replica Placement for Scalable Content Delivery,” Proc. First Int'l Workshop Peer-to-Peer Systems, pp. 306-318, 2002.
[7] Y. Chen, R. Katz, and J. Kubiatowicz, “SCAN: A Dynamic Scalable and Efficient Content Distribution Network,” Proc. First Int'l Conf. Pervasive Computing, 2002.
[8] S. Jamin, C. Jiu, A. Kurc, D. Raz, and Y. Shavitt, “Constrained Mirror Placement on the Internet,” Proc. IEEE INFOCOM, vol. 1, pp. 31-40, Apr. 2001.
[9] M. Sayal, Y. Breitbart, P. Scheuermann, and R. Vingralek, “Selection Algorithms for Replicated Web Servers,” Proc. Workshop Internet Server Performance, 1998.
[10] X. Tang and J. Xu, “On Replica Placement for QoS-Aware Content Distribution,” Proc. IEEE INFOCOM, vol. 2, pp. 806-815, Mar. 2004.
[11] X. Tang and S. Chanson, “The Minimal Cost Distribution Tree Problem of Recursive Expiration-Based Consistency Management,” IEEE Trans. Parallel and Distributed Systems, vol. 15, no. 3, pp. 214-227, Mar. 2004.
[12] X. Tang and S. Chanson, “Minimal Cost Replication of Dynamic Web Contents under Flat Update Delivery,” IEEE Trans. Parallel and Distributed Systems, vol. 15, no. 5, pp. 431-439, May 2004.
[13] E. Cohen and S. Shenker, “Replication Strategies in Unstructured Peer-to-Peer Networks,” Proc. ACM SIGCOMM, 2002.
[14] M.R. Garey and D.S. Johnson, Computers and Intractability. A Guide to the Theory on NP-Completeness. W.H. Freeman and Company, 1979.
[15] H. Kellerer, U. Pferschy, and D. Pisinger, Knapsack Problems. Spinger-Verlag, 2004.
[16] F. Chudak and D. Williamson, “Improved Approximation Algorithms for Capacitated Facility Location Problems,” Proc. Seventh Conf. Integer Programming and Combinatorial Optimization, pp. 99-113, 1999.
[17] M. Korupolu, C. Plaxton, and R. Rajaraman, “Analysis of a Local Search Heuristic for Facility Location Problems,” J. Algorithms, vol. 37, pp. 146-188, 2000.
[18] V. Arya, N. Garg, R. Khandekar, K. Munagala, and V. Pandit, “Local Search Heuristics for K-Median and Facility Location Problems,” Proc. 33rd ACM Symp. Theory of Computing, pp. 21-29, 2001.
[19] K. Jain and V. Vazirani, “Approximation Algorithms for the Metric Facility Location and K-Median Problems Using the Primal-Dual Schema and the Lagrangian Relaxation,” J. ACM, vol. 48, pp. 274-296, 2001.
[20] M. Pal, I. Tardos, and T. Wexler, “Facility Location with Nonuniform Hard Capacities,” Proc. IEEE Symp. Foundations of Computer Science, p. 329, Oct. 2001.
[21] F. Chudak and D. Shmoys, “Improved Approximation Algorithms for the Uncapacitated Facility Location Problem,” SIAM J. Computing, vol. 33, no. 1, pp. 1-25, 2003.
[22] M. Hajiaghavi, M. Mahdian, and V.S. Mirrokni, “The Facility Location Problem with General Cost Functions,” Networks, vol. 42, no. 1, pp. 42-47, 2003.
[23] S. Siachalou and L. Georgiadis, “Efficient QoS Routing,” Computer Networks, vol. 43, pp. 351-367, 2003.
[24] P. van Mieghem, H. de Neve, and F. Kuipers, “Hop-by-Hop Quality of Service Routing,” Computer Networks, vol. 37, pp. 407-423, 2001.
[25] R. Andonov and S. Rajopadhye, “A Sparse Knapsack Algo-Tech-Cuit and Its Synthesis,” Proc. IEEE Int'l Conf. Application Specific Array Processors, pp. 302-313, Aug 1994.
[26] M. Mahdian, E. Markakis, A. Saberi, and V. Varizani, “Greedy Facility Location Algorithms Analyzed Using Dual Fitting with Factor-Revealing LP,” J. ACM, vol. 50, no. 6, pp. 795-824, 2003.
[27] G. Rodolakis, S. Siachalou, and L. Georgiadis, “Replicated Server Placement with QoS Constraints,” , 2005.
[28] R. Hassin, “Approximation Schemes for the Restricted Shortest Path Problem,” Math. of Operations Research, vol. 17, no. 1, pp. 36-42, 1992.
[29] D. Lorenz and D. Raz, “A Simple Efficient Approximation Scheme for the Restricted Shortest Path Problem,” Operations Research Letters, vol. 28, no. 5, pp. 213-221, June 2001.
[30] M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf, Computational Geometry, Algorithms and Applications. Springer-Verlag, 2000.
[31] A. Medina, A. Lakhina, I. Matta, and J. Byers, “BRITE: Universal Topology Generation from a User's Perspective,” Technical Report 2001-003, 2001.

Index Terms:
Algorithm design and analysis, constrained optimization, applications, distributed file systems, client/server.
Georgios Rodolakis, Stavroula Siachalou, Leonidas Georgiadis, "Replicated Server Placement with QoS Constraints," IEEE Transactions on Parallel and Distributed Systems, vol. 17, no. 10, pp. 1151-1162, Oct. 2006, doi:10.1109/TPDS.2006.145
Usage of this product signifies your acceptance of the Terms of Use.