Abstract
In this paper, we propose a fast heuristic algorithm for the maximum concurrent k-splittable flow problem. In such an optimization problem, one is concerned with maximizing the routable demand fraction across a capacitated network, given a set of commodities and a constant k expressing the number of paths that can be used at most to route flows for each commodity. Starting from known results on the k-splittable flow problem, we design an algorithm based on a multistart randomized scheme which exploits an adapted extension of the augmenting path algorithm to produce starting solutions for our problem, which are then enhanced by means of an iterative improvement routine. The proposed algorithm has been tested on several sets of instances, and the results of an extensive experimental analysis are provided in association with a comparison to the results obtained by a different heuristic approach and an exact algorithm based on branch and bound rules.
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References
Ahuja R.K., Magnanti T.L., Orlin J.B.: Network Flows: Theory Algorithms and Applications. Prentice Hall Inc., Englewood Cliffs (1993)
Albrecht C.: Global routing by new approximation algorithms for multicommodity flow. IEEE Trans. Comput. Aided Des. Integr. Circuit Syst. 20, 622–632 (2001)
Andrews, M., Zhang, L.: Hardness of the undirected congestion minimization problem. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing (2005)
Azar, Y., Regev, O.: Strongly polynomial algorithms for the unsplittable flow problem. In: Proceedings of the 8th Conference on Integer Programming and Combinatorial Optimization, pp. 15–29 (2001)
Badics, T.: GENRMF. (1991). ftp://dimacs.rutgers.edu/pub/netflow/generators/network/genrmf/
Bienstock D., Raskina O.: Asymptotic analysis of the flow deviation method for the maximum concurrent flow problem. Math. Program. Ser. B 91, 479–492 (2002)
Baier G., Köhler E., Skutella M.: On the k-splittable flow problem. Algorithmica 42, 231–248 (2005)
Caramia M., Sgalambro A.: An exact approach for the maximum concurrent k-splittable flow problem. Optim. Lett. 2(2), 251–265 (2008)
Caramia M., Sgalambro A.: On the approximation of the single source k-splittable flow problem. J. Discrete Algorithms 6(2), 277–289 (2008)
Chuzhoy, J., Naor, J.: New hardness results for congestion minimization and machine scheduling. In: Proceedings of the 36th Annual ACM Symposium of Theory of Computing, pp. 28–34, Chicago, IL (2004)
Dinitz Y., Garg N., Goemans M.X.: On the single-source unsplittable flow problem. Combinatorica 19, 17–41 (1999)
Fratta, L., Gerla, M., Kleinrock, L.: The flow deviation method: an approach to store-and-forward computer-communication network design. Networks 3 (1973)
Goldfarb D., Grigoriadis M.: A computational comparison of the Dinic and network simplex methods for maximum flow. Ann. Oper. Res. 13, 83–123 (1988)
Guruswami, V., Khanna, S., Rajaraman, R., Sheperd, B., Yannakakis, M.: Near optimal hardness results and approximation algorithms for edge-disjoint paths and related problems. In: Proceedings of the 31st Annual ACM Symposium on Theory of Computing, pp. 19–28 (1999)
Hu J., Sapatnekar S.S.: A survey on multi-net global routing for integrated circuits. Integration VLSI J. 31, 1–49 (2001)
Kleinberg, J.: Approximation algorithms for disjoint paths problems. PhD thesis, MIT (1996)
Kleinberg, J.: Single-source unsplittable flow. In: Proceedings of the 37th Annual Symposium on Foundations of Computer Science, pp. 68–77 (1996)
Kleinberg, J., Tardos, E.: Disjoint paths in densely embedded graphs. In: Proceedings of the 36th Annual Symposium on Foundations of Computer Science, pp. 52–61 (1995)
Koch, R., Skutella, M., Spenke, I.: Approximation and complexity of k-splittable flows. Technical Report (2005)
Kolliopoulos, S.G.: Improved approximation algorithms for unsplittable flow problems. In: Proceedings of the 38th Annual Symposium on Foundations of Computer Science, pp. 426–435 (1997)
Kolliopoulos S.G.: Minimum-cost single-source 2-splittable flow. Inf. Process. Lett. 9(1), 15–18 (2005)
Kolman, P., Scheideler, C.: Improved bounds for the unsplittable flow problem. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 184–193 (2002)
Martens M., Skutella M.: Flows on few paths: algorithms and lower bounds. Networks 48(2), 68–76 (2006)
Müller, D.: Optimizing Yield in Global Routing. ICCAD (2006)
Raghavan P., Thompson C.: Randomized rounding: a technique for provable good algorithms and algorithmic proofs. Combinatorica 7(4), 365–374 (1987)
Raghavan P., Thompson C.: Multiterminal global routing: a deterministic approximation scheme. Algorithmica 6, 73–82 (1991)
Shahrokhi F., Matula D.W.: The maximum concurrent flow problem. J ACM 37, 318–334 (1990)
Skutella M.: Approximating the single source unsplittable min-cost flow problem. Math. Programm. 91, 493–514 (2002)
Vygen, J.: Near-optimum global routing with coupling, delay bounds, and power consumption. In: Proceedings of the 10th International IPCO Conference, pp. 308–324. Springer, New York (2004)
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Caramia, M., Sgalambro, A. A fast heuristic algorithm for the maximum concurrent k-splittable flow problem. Optim Lett 4, 37–55 (2010). https://doi.org/10.1007/s11590-009-0147-4
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DOI: https://doi.org/10.1007/s11590-009-0147-4