# Light-trail based Hierarchy - The Optimal Multicast Route in WDM Networks Without Splitters and Converters

### Dinh Danh Le, Massinissa Merabet

#### Abstract

Multicasting in WDM core networks is known as an efficient way of communications in high-speed multimedia applications. However, costly and complicated fabrication prevents multicast capable switches (splitters) from deploying in the proposed architectures. Besides, in practical routing cases, the state of the network is given by a directed graph. Accordingly, this paper investigates the multicast routing without splitters in directed asymmetric topologies. The objective is to minimize the number of wavelengths used and then find the best cost solution among those requiring the same number of wavelengths. In the case of no splitters, a set of light-paths starting from the multicast source covering all the destinations is known as the traditional solution. In this paper, we introduce two new concepts namely light-trail based hierarchy and light-path based hierarchy, and develop two ILP formulations for them. Theoretical analysis and simulation results show that the optimal solution is a set of light-trail based hierarchies. Particularly, our light-trail based solution achieves fewer wavelengths required (up to 21.95% saved) while keeping slightly lower cost (up to 3.79% saved) compared to light-path based solution.

#### References

- Ali, M. and Deogun, J. S. (2000a). Cost-effective implementation of multicasting in wavelength-routed networks. IEEE/OSA Journal of Lightwave Technology, 18:1628-1638.
- Ali, M. and Deogun, J. S. (2000b). Power-efficient design of multicast wavelength routed networks. IEEE Journal on Selected Areas in Communications, 18:1852-1862.
- Din, D.-R. (2009). Heuristic Algorithms for Finding LightForest of Multicast Routing on WDM Network. Information Science and Engineering, 25:83-103.
- Garey, M. R. and Johnson, D. S. (1979). Computers and Intractability: A Guide to the Theory of NPCompleteness. W. H. Freeman & Co, New York, NY, USA.
- Le, D. D., Molnar, M., and Palaysi, J. (2013). Multicast Routing in WDM without Splitters. Infocommunications Journal, 5(2):1-10.
- Li, D., Du, X., Hu, X., Ruan, L., and Jia, X. (2000). Minimizing number of wavelengths in multicast routing trees in WDM networks. Networks, 35(4):260-265.
- Makhorin, A. O. (2010). GNU Linear Programming Kit (GLPK).
- Mehlhorn, K. and Naeher, S. (2010). LEDA-a Library of Efficient Data Types and Algorithms.
- Molnar, M. (2011). Hierarchies to Solve Constrained Connected Spanning Problems. Technical Report 11029, LIRMM.
- Mukherjee, B. (2006). Optical WDM Networks. Springer.
- Yu, O. and Cao, Y. (2005). Mathematical formulation of optical multicast with loss-balanced lightforest. In Global Telecommunications Conference, 2005. GLOBECOM 7805. IEEE, volume 4, pages 5 pp.- 1972.
- Zhang, X., Wei, J., and Qiao, C. (2000). Constrained multicast routing in WDM networks with sparse light splitting. IEEE/OSA Journal of Lightwave Technology, 18:1917-1927.
- Zhou, F., Molnar, M., and Cousin, B. (2010). LightHierarchy: The Optimal Structure for Multicast Routing in WDM Mesh Networks. In Computers and Communications (ISCC), 2010 IEEE Symposium on The 15th IEEE Symposium on Computers and Communications (ISCC2010), 2010, pages 611 - 616, Riccione Italie.
- Zhou, Y. and Poo, G.-S. (2005). Optical multicast over wavelength-routed WDM networks: A survey. Optical Switching and Networking, 2(3):176 - 197.

#### Paper Citation

#### in Harvard Style

Le D. and Merabet M. (2014). **Light-trail based Hierarchy - The Optimal Multicast Route in WDM Networks Without Splitters and Converters** . In *Proceedings of 2nd International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS,* ISBN 978-989-758-008-6, pages 66-73. DOI: 10.5220/0004705300660073

#### in Bibtex Style

@conference{photoptics14,

author={Dinh Danh Le and Massinissa Merabet},

title={Light-trail based Hierarchy - The Optimal Multicast Route in WDM Networks Without Splitters and Converters},

booktitle={Proceedings of 2nd International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS,},

year={2014},

pages={66-73},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004705300660073},

isbn={978-989-758-008-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of 2nd International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS,

TI - Light-trail based Hierarchy - The Optimal Multicast Route in WDM Networks Without Splitters and Converters

SN - 978-989-758-008-6

AU - Le D.

AU - Merabet M.

PY - 2014

SP - 66

EP - 73

DO - 10.5220/0004705300660073