Abstract
We present mixed integer programming approaches for optimally solving a combinatorial optimization problem arising in network design with additional quality of service constraints. The rooted delay- and delay-variation-constrained Steiner tree problem asks for a cost-minimal Steiner tree satisfying delay-constraints from source to terminals and a maximal variation-bound between particular terminal path-delays. Our MIP models are based on multi-commodity-flows and a layered graph transformation. For the latter model we propose some new sets of valid inequalities and an efficient separation method. Presented experimental results indicate that our layered graph approaches clearly outperform the flow-based model.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network flows: theory, algorithms, and applications. Prentice Hall (1993)
Cherkassky, B.V., Goldberg, A.V.: On Implementing the Push-Relabel Method for the Maximum Flow Problem. Algorithmica 19(4), 390–410 (1997)
Gouveia, L.: Multicommodity flow models for spanning trees with hop constraints. European Journal of Operational Research 95(1), 178–190 (1996)
Gouveia, L., Paias, A., Sharma, D.: Modeling and solving the rooted distance-constrained minimum spanning tree problem. Computers & Operations Research 35(2), 600–613 (2008)
Gouveia, L., Simonetti, L.G., Uchoa, E.: Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs. Mathematical Programming 128(1), 123–148 (2011)
Haberman, B.K., Rouskas, G.N.: Cost, delay, and delay variation conscious multicast routing. Tech. rep., North Carolina State University (1996)
Koch, T., Martin, A.: Solving Steiner tree problems in graphs to optimality. Networks 32(3), 207–232 (1998)
Kun, Z., Heng, W., Feng-yu, L.: Distributed multicast routing for delay and delay variation-bounded Steiner tree using simulated annealing. Computer Communications 28(11), 1356–1370 (2005)
Lee, H.-Y., Youn, C.-H.: Scalable multicast routing algorithm for delay-variation constrained minimum-cost tree. In: IEEE International Conference on Communications, vol. 3, pp. 1343–1347. IEEE Press (2000)
Ljubic, I., Weiskircher, R., Pferschy, U., Klau, G.W., Mutzel, P., Fischetti, M.: An algorithmic framework for the exact solution of the prize-collecting Steiner tree problem. Mathematical Programming 105(2), 427–449 (2006)
Low, C.P., Lee, Y.J.: Distributed multicast routing, with end-to-end delay and delay variation constraints. Computer Communications 23(9), 848–862 (2000)
Rouskas, G.N., Baldine, I.: Multicast routing with end-to-end delay and delay variation constraints. IEEE Journal on Selected Areas in Communications 15(3), 346–356 (1997)
Ruthmair, M., Raidl, G.R.: Variable Neighborhood Search and Ant Colony Optimization for the Rooted Delay-Constrained Minimum Spanning Tree Problem. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI, Part II. LNCS, vol. 6239, pp. 391–400. Springer, Heidelberg (2010)
Ruthmair, M., Raidl, G.R.: A Layered Graph Model and an Adaptive Layers Framework to Solve Delay-Constrained Minimum Tree Problems. In: Günlük, O., Woeginger, G.J. (eds.) IPCO 2011. LNCS, vol. 6655, pp. 376–388. Springer, Heidelberg (2011)
Sheu, P.-R., Chen, S.-T.: A fast and efficient heuristic algorithm for the delay- and delay variation-bounded multicast tree problem. Computer Communications 25(8), 825–833 (2002)
Sheu, P.-R., Tsai, H.-Y., Chen, S.-C.: An Optimal MILP Formulation for the Delay- and Delay Variation-Bounded Multicast Tree Problem. Journal of Internet Technology 8(3), 321–328 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ruthmair, M., Raidl, G.R. (2012). On Solving the Rooted Delay- and Delay-Variation-Constrained Steiner Tree Problem. In: Mahjoub, A.R., Markakis, V., Milis, I., Paschos, V.T. (eds) Combinatorial Optimization. ISCO 2012. Lecture Notes in Computer Science, vol 7422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32147-4_21
Download citation
DOI: https://doi.org/10.1007/978-3-642-32147-4_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32146-7
Online ISBN: 978-3-642-32147-4
eBook Packages: Computer ScienceComputer Science (R0)