A Layered Graph Model and an Adaptive Layers Framework to Solve Delay-Constrained Minimum Tree Problems
We present a layered graph model for delay-constrained minimum tree problems with a polynomial number of constraints which can be solved well for instances with low- to medium-sized sets of achievable delay values and not too high bounds. Layered graph models have been recently shown to frequently yield tight bounds in the context of hop- or delay-constrained network design problems. However, since the size of the layered graph heavily depends on the size of the set of achievable delay values and the corresponding delay bound the practical applicability of these models is limited. To overcome this problem we introduce an iterative strategy in which an initially small layered graph is successively extended in order to tighten lower and upper bounds until convergence to the optimal solution. Computational results show the synergetic effectiveness of both approaches outperforming existing models in nearly all cases.
KeywordsInteger Linear Programming Layered Graph Steiner Tree Variable Neighborhood Search Linear Programming Relaxation
Unable to display preview. Download preview PDF.
- 3.Gouveia, L., Simonetti, L., Uchoa, E.: Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs. Mathematical Programming, pp. 1–26 (2010)Google Scholar
- 5.Gouveia, L.: Using hop-indexed models for constrained spanning and Steiner tree models, pp. 21–32. Kluwer Academic Publishers, Dordrecht (1999)Google Scholar
- 10.Ljubic, I., Gollowitzer, S.: Modelling the hop constrained connected facility location problem on layered graphs. In: Electronic Notes in Discrete Mathematics, vol. 36, pp. 207–214. Elsevier, Amsterdam (2010)Google Scholar
- 12.Manyem, P., Stallmann, M.: Some approximation results in multicasting. Tech. Rep. TR-96-03, North Carolina State University (1996)Google Scholar
- 14.Robins, G., Zelikovsky, A.: Improved Steiner tree approximation in graphs. In: SODA 2000: Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms, pp. 770–779. Society for Industrial and Applied Mathematics (2000)Google Scholar
- 16.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. LNCS, vol. 6239, pp. 391–400. Springer, Heidelberg (2010)Google Scholar
- 17.Xu, Y., Qu, R.: A GRASP approach for the Delay-constrained Multicast routing problem. In: Proceedings of the 4th Multidisplinary International Scheduling Conference (MISTA4), Dublin, Ireland, pp. 93–104 (2009)Google Scholar
- 18.Xu, Y., Qu, R.: A hybrid scatter search meta-heuristic for delay-constrained multicast routing problems. Applied Intelligence, 1–13 (2010)Google Scholar