Abstract
Modern life heavily relies on communication networks that operate efficiently. A crucial issue for the design of communication networks is robustness with respect to traffic fluctuations, since they often lead to congestion and traffic bottlenecks. In this paper, we address an NP-hard single commodity robust network design problem, where the traffic demands change over time. For k different times of the day, we are given for each node the amount of single-commodity flow it wants to send or to receive. The task is to determine the minimum-cost edge capacities such that the flow can be routed integrally through the net at all times. We present an exact branch-and-cut algorithm, based on a decomposition into biconnected network components, a clever primal heuristic for generating feasible solutions from the linear-programming relaxation, and a general cutting-plane separation routine that is based on projection and lifting. By presenting extensive experimental results on realistic instances from the literature, we show that a suitable combination of these algorithmic components can solve most of these instances to optimality. Furthermore, cutting-plane separation considerably improves the algorithmic performance.
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References
ABACUS – A Branch-And-CUt System, http://www.informatik.uni-koeln.de/abacus
LEDA – Library of Efficient Data Types and Algorithms, http://www.algorithmic-solutions.com
ILOG CPLEX 12.1 (2009), http://www.ilog.com/products/cplex
SCIL 0.9 (2011), http://www.scil-opt.net
Altin, A., Amaldi, E., Belotti, P., Pinar, M.: Provisioning virtual private networks under traffic uncertainty. Networks 49(1), 100–115 (2007)
Applegate, A., Bixby, R., Chvátal, V., Cook, W.: TSP cuts which do not conform to the template paradigm. In: Jünger, M., Naddef, D. (eds.) Computational Combinatorial Optimization. LNCS, vol. 2241, pp. 261–304. Springer, Heidelberg (2001)
Ben-Ameur, W., Kerivin, H.: Routing of uncertain demands. Optimization and Engineering 3, 283–313 (2005)
Buchheim, C., Liers, F., Oswald, M.: Local cuts revisited. Operations Research Letters 36(4), 430–433 (2008)
Buchheim, C., Liers, F., Oswald, M.: Speeding up IP-based algorithms for constrained quadratic 0–1 optimization. Mathematical Programming (Series B) 124(1-2), 513–535 (2010)
Chekuri, C.: Routing and network design with robustness to changing or uncertain traffic demands. SIGACT News 38(3), 106–128 (2007)
Chvátal, V.: Linear programming. Series of books in the mathematical sciences. W.H. Freeman, New York (1983)
Duffield, N., Goyal, P., Greenberg, A., Mishra, P., Ramakrishnan, K., van der Merwe, J.: A flexible model for resource management in virtual private networks. Proceedings of SIGCOMM 29, 95–108 (1999)
Eisenbrand, F., Grandoni, F., Oriolo, G., Skutella, M.: New approaches for virtual private network design. SIAM Journal on Computing, 706–721 (2007)
Erlebach, T., Rüegg, M.: Optimal bandwidth reservation in hose-model VPNs with multi-path routing. Proceedings of INFOCOM 4, 2275–2282 (2004)
Fakcharoenphol, J., Rao, S., Talwar, K.: A tight bound on approximating arbitrary metrics by tree metrics. In: Proceedings of the 35th Annual ACM Symposium on Theory of Computing, pp. 448–455 (2003)
Fingerhut, J., Suri, S., Turner, J.: Designing least-cost nonblocking broadband networks. Journal of Algorithms 24(2), 287–309 (1997)
Fiorini, S., Oriolo, G., Sanità, L., Theis, D.: The VPN problem with concave costs. SIAM Journal on Discrete Mathematics, 1080–1090 (2010)
Gomory, R., Hu, T.: Multi-terminal network flow. SIAM Journal on Applied Mathematics 9, 551–570 (1961)
Goyal, N., Olver, N., Shepherd, B.: The VPN conjecture is true. In: Proceedings of STOC, pp. 443–450 (2008)
Gupta, A., Kleinberg, J., Rastogi, R., Yener, B.: Provisioning a virtual private network: A network design problem for multicommodity flow. In: Proceedings of STOC, pp. 389–398 (2001)
Gupta, A., Kumar, A., Roughgarden, T.: Simpler and better approximation algorithms for network design. In: Proceedings of STOC, pp. 365–372 (2003)
Jain, K.: A factor 2 approximation algorithm for the generalized Steiner network problem. In: Proceedings of the 39th Annual Symposium on Foundations of Computer Science (FOCS) (1998)
Labbe, M., Séguin, R., Soriano, P., Wynants, C.: Network synthesis with non-simultaneous multicommodity flow requirements: Bounds and heuristics (1999)
Magnanti, T., Raghavan, S.: Strong formulations for network design problems with connectivity requirements. Networks 45, 61–79 (2005)
Magnanti, T., Wang, Y.: Polyhedral properties of the network restoration problem with the convex hull of a special case. Tech. rep., Operations Research Center, MIT (1997)
Minoux, M.: Robust network optimization under polyhedral demand uncertainty is NP-hard. Discrete Applied Mathematics, 597–603 (2010)
Sanità, L.: Robust Network Design. Ph.D. Thesis, Università Sapienza di Roma (2009)
Sridhar, S., Chandrasekaran, R.: Integer solution to synthesis of communication networks. Mathematics of Operations Research 3, 581–585 (1992)
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Buchheim, C., Liers, F., Sanità, L. (2011). An Exact Algorithm for Robust Network Design. In: Pahl, J., Reiners, T., Voß, S. (eds) Network Optimization. INOC 2011. Lecture Notes in Computer Science, vol 6701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21527-8_2
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DOI: https://doi.org/10.1007/978-3-642-21527-8_2
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