# Two Heuristics for Calculating a Shared Risk Link Group Disjoint Set of Paths of Min-Sum Cost

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## Abstract

A shared risk link group (SRLG) is a set of links which share a common risk of failure. Routing protocols in Generalized MultiProtocol Label Switching, using distributed SRLG information, can calculate paths avoiding certain SRLGs. For single SRLG failure an end-to-end SRLG-disjoint path pair can be calculated, but to ensure connection in the event of multiple SRLG failures a set with more than two end-to-end SRLG-disjoint paths should be used. Two heuristic, the Conflicting SRLG-Exclusion Min Sum (CoSE-MS) and the Iterative Modified Suurballes’s Heuristic (IMSH), for calculating node and SRLG-disjoint path pairs, which use the Modified Suurballes’s Heuristic, are reviewed and new versions (CoSE-MScd and IMSHd) are proposed, which may improve the number of obtained optimal solutions. Moreover two new heuristics are proposed: kCoSE-MScd and kIMSHd, to calculate a set of \(k\) node and SRLG-disjoint paths, seeking to minimize its total cost. To the best of our knowledge these heuristics are a first proposal for seeking a set of \(k\, (k>2)\) node and SRLG-disjoint paths of minimal additive cost. The performance of the proposed heuristics is evaluated using a real network structure, where SRLGs were randomly defined. The number of solutions found, the percentage of optimal solutions and the relative error of the sub-optimal solutions are presented. Also the CPU time for solving the problem in a path computation element is reported.

## Keywords

Diverse routing SRLG-disjoint Node-disjoint Min-sum## Notes

### Acknowledgments

The author acknowledges financial support through project QREN 23301 PANORAMA II, co-financed by European Union’s FEDER through “Programa Operacional Factores de Competitividade” (POFC) of QREN (FCOMP-01-0202-FEDER-023301) by the Portuguese Foundation for Science and Technology under project grant PEst-OE/EEI/UI308/2014 and by Project PERGS of Portugal Telecom Inovação. We thank the anonymous referees for their comments and suggestions, which contributed to improve the paper.

## References

- 1.Mouftah, H.T., Ho, P.-H.: Optical networks: arquitecture and survivability. Kluwer Academic Publishers, Dordrecht (2003)CrossRefGoogle Scholar
- 2.Tapolcai, J., Pin-Han Ho, D., Verchere, T.Cinkler: A new shared segment protection method for survivable networks with guaranteed recovery time. IEEE Trans. Reliab.
**57**(2), 272–282 (2008)CrossRefGoogle Scholar - 3.Jaumard, B., Nahar Bhuiyan, N., Sebbah, S., Huc, F., Coudert , D.: A new framework for efficient shared segment protection scheme for WDM networks. In: International Conference on High Performance Switching and Routing (HPSR), 2010, pp. 189–196. (2010)Google Scholar
- 4.Medhi, D., Sankarappan, S.: Impact of a transmission facility link failure on dynamic call routing cicuit-switched networks under various circuit layout policies. J. Netw. Syst. Manag.
**1**(2), 143–169 (1993)CrossRefGoogle Scholar - 5.Rajagopalan, B., Pendarakis, D., Saha, D., Ramamoorthy, R.S.: IP over optical networks: architectural aspects. IEEE Commun. Mag.
**38**(9), 94–102 (2000)CrossRefGoogle Scholar - 6.Vasseur, J.-P., Pickavet, M., Demeester, P.: Network Recovery: Protection and Restoration of Optical, SONET-SDH, IP, and MPLS. Elsevier, Amsterdam (2004)Google Scholar
- 7.Braden, R., Zhang, L., Berson, S., Herzog, S., Jamin, S.: Resource reservation protocol (RSVP—version 1 functional specification. IETF RFC 2205). (1997)Google Scholar
- 8.Awduche, D., Berger, L., Gan, D., Li, T., Srinivasan, V., Swallow, G.: RSVP-TE: extensions to RSVP for LSP tunnels. IETF RFC 3209. (2001)Google Scholar
- 9.Zhang, F., Li, D., Gonzalez de Dios, O., Margaria, C.: RSVP-TE extensions for collecting SRLG information. IETF Draft. (2014)Google Scholar
- 10.Kompella, K., Rekhter, Y.: Routing extensions in support of generalized multi-protocol label switching (GMPLS). IETF RFC 4202. (2005)Google Scholar
- 11.Farrel, A., Vasseur, J.-P., Ash, J.: A path computation element (PCE)-based architecture. ITEF RFC 4655. (2006)Google Scholar
- 12.Saturio, M. C., López, V., Dios, Ó. G., del Nuevo, F. M., Fernández-Palacios, J. P.: Implementation and assessment of pre-reservation mechanism for PCE environments. J. Netw. Syst. Manag.
**22**(3), 488–508 (2014)Google Scholar - 13.Suurballe, J.W., Tarjan, R.E.: A quick method for finding shortest pairs of disjoint paths. Networks
**14**(2), 325–336 (1984)MathSciNetCrossRefGoogle Scholar - 14.Bhandari, R.: Survivable Networks, Algorithms for Diverse Routing. Kluwer Academic Publishers, Norwell, MA (1999)zbMATHGoogle Scholar
- 15.Xu, D., Chen, Y., Xiong, Y., Qiao, C., He, X.: On finding disjoint paths in single and dual link cost networks. In: IEEE INFOCOM 2004. Hong Kong (2004)Google Scholar
- 16.Kodialam, M., Lakshman, T.V.: Dynamic routing of bandwidth guaranteed tunnels with restoration. IEEE INFOCOM
**2000**, 902–911 (2000)Google Scholar - 17.Laborczi, P., Tapolcai, J., Ho, P.-H., Cinkler, T., Recski, A., Mouftah, H.T.: Algorithms for asymmetrically weighted pair of disjoint paths in survivable networks. In: Cinkler, T. (ed.) Proceedings of Design of Reliable Communication Networks (DRCN), pp. 220–227. Budapest, Hungary (2001)Google Scholar
- 18.Gan, Ming-Lee, Liew, Soung-Yue: Effective algorithms for finding optimum pairs of link-disjoint paths in \(\alpha +1\) path protection. Telecommun. Syst.
**52**(2), 783–797 (2013)Google Scholar - 19.Li, C.L., McCormick, S.T., Simchi-Levi, D.: The complexity of finding two disjoint paths with min–max objective function. Discret. Appl. Math.
**26**(1), 105–115 (1990)zbMATHMathSciNetCrossRefGoogle Scholar - 20.Gomes, T., Craveirinha, J., Jorge, L.: An effective algorithm for obtaining the minimal cost pair of disjoint paths with dual arc costs. Comput. Oper. Res.
**36**(5), 1670–1682 (2009)zbMATHMathSciNetCrossRefGoogle Scholar - 21.Rak, J.: \(k\)-Penalty: a novel approach to find \(k\)-disjoint paths with differentiated path costs. Commun. Lett. IEEE
**14**(4), 354–356 (2010)CrossRefGoogle Scholar - 22.Hu, J.Q.: Diverse routing in optical mesh networks. IEEE Trans. Commun.
**51**(3), 489–494 (2003)CrossRefGoogle Scholar - 23.Oki, E., Matsuura, N., Shiomoto, K., Yamanaka, N.: A disjoint path selection scheme with shared risk link groups in GMPLS networks. IEEE Commun. Lett.
**6**(9), 406–408 (2002)CrossRefGoogle Scholar - 24.Xu, D., Xiong, Y., Qiao, C., Li, G.: Trap avoidance and protection schemes in networks with shared risk link groups. J. Lightwave Technol.
**21**(11), 2683–2693 (2003)CrossRefGoogle Scholar - 25.Ho, P.-H., Mouftah, H.T.: Shared protection in mesh WDM networks. IEEE Commun. Mag.
**42**(1), 70–76 (2004)CrossRefGoogle Scholar - 26.Rostami, M.J., Khorsandi, S., Khodaparast, A.A.: CoSE: A SRLG-disjoint routing algorithm. In: Proceedings of the Fourth European Conference on Universal Multiservice Networks (ECUMN’07). Toulouse (2007)Google Scholar
- 27.Gomes, T., Fernandes, L.: Obtaining a SRLG-disjoint path pair of min-sum cost. In: Rak, J., Tipper, D., Walkowiak, K. (eds.) RNDM 2010–2nd International Workshop on Reliable Networks Design and Modeling, colocated with ICUMT 2010. ISBN: 978-I-4244-7283-3, pp. 116–122. Moscow (2010)Google Scholar
- 28.Gomes, T., Simões, C., Fernandes, L.: Resilient routing in optical networks using SRLG-disjoint path pairs of min-sum cost. Telecommun. Syst. J.
**52**(2), 737–749 (2013)Google Scholar - 29.Todimala, A., Ramamurthy, B.: IMSH: An iterative heuristic for SRLG diverse routing in WDM mesh networks. In: Proceedings of the 13th International Conference on Computer Communications and Networks, ICCCN’2004, pp. 199–204. (2004)Google Scholar
- 30.Ho, P.-H., Tapolcai, J., Mouftah, H.T.: On achieving optimal survivable routing for shared protection in survivable next-generation internet. IEEE Trans. Reliab.
**53**(2), 216–225 (2004)CrossRefGoogle Scholar - 31.Datta, Pallab, Somani, Arun K.: Graph transformation approaches for diverse routing in shared risk resource group (srrg) failures. Comput. Netw.
**52**(12), 2381–2394 (2008)zbMATHCrossRefGoogle Scholar - 32.Lee, H.-W., Modiano, E., Lee, K.: Diverse routing in networks with probabilistic failures. IEEE/ACM Trans. Netw.
**18**(6), 1895–1907 (2010)CrossRefGoogle Scholar - 33.Diaz, O., Xu, F., Min-Allah, N., Khodeir, M., Peng, M., Khan, S., Ghani, N.: Network survivability for multiple probabilistic failures. Commun. Lett. IEEE
**16**(8), 1320–1323 (2012)zbMATHCrossRefGoogle Scholar - 34.Xu, D., Li, G., Ramamurthy, B., Chiu, A., Wang, D., Doverspike, R.: SRLG-diverse routing of multiple circuits in a heterogeneous optical transport network. In: Proceedings of the 8th International Workshop on the Design of Reliable Communication Networks (DRCN 2011), pp. 180–187. (2011)Google Scholar
- 35.Xu, Dahai, Li, Guangzhi, Ramamurthy, Byrav, Chiu, Angela, Wang, Dongmei, Doverspike, Robert: On provisioning diverse circuits in heterogeneous multi-layer optical networks. Comput. Commun.
**36**(6), 689–697 (2013). Reliable Network-based Services.CrossRefGoogle Scholar - 36.Habib, M.F., Tornatore, M., De Leenheer, M., Dikbiyik, F., Mukherjee, B.: Design of disaster-resilient optical datacenter networks. J. Lightwave Technol.
**30**(16), 2563–2573 (2012)zbMATHCrossRefGoogle Scholar - 37.Develder, C., Buysse, J., De Leenheer, M., Jaumard, B., Dhoedt, B.: Resilient network dimensioning for optical grid/clouds using relocation. In: IEEE International Conference on Communications (ICC), 2012, pp 6262–6267. (2012)Google Scholar
- 38.Yen, J.Y.: Finding the \(k\) shortest loopless paths in a network. Manag. Sci.
**17**(11), 712–716 (1971)zbMATHCrossRefGoogle Scholar - 39.Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math.
**1**, 269–271 (1959)zbMATHMathSciNetCrossRefGoogle Scholar - 40.Kuipers, F.A., Korkmaz, T., Krunz, M., Van Mieghem, P.: A review of constraint-based routing algorithms. Technical report, Delft University of Technology, (2002)Google Scholar
- 41.Clímaco, J., Craveirinha, J.: On OR-based routing approaches for the Internet. Int. Trans. Oper. Res.
**18**(3), 295–305 (2011)MathSciNetCrossRefGoogle Scholar - 42.Martins, E., Pascoal, M.: A new implementation of Yen’s ranking loopless paths algorithm. 4OR Q. J. Belg. Fr. Ital. Oper. Res. Soc.
**1**(2), 121–134 (2003)zbMATHMathSciNetGoogle Scholar - 43.Martins, E., Pascoal, M., Santos, J.: Deviation algorithms for ranking shortest paths. Int. J. Found. Comput. Sci.
**10**(3), 247–263 (1999)CrossRefGoogle Scholar - 44.Martins, E., Pascoal, M., Santos, J.: An algorithm for ranking loopless paths. Technical Report 99/007, CISUC. (1999)Google Scholar
- 45.Clímaco, J., Craveirinha, J., Pascoal, M.: A bicriterion approach for routing problems in multimedia networks. Networks
**41**(4), 206–219 (2003)MathSciNetCrossRefGoogle Scholar - 46.Liu, Chang, Ruan, Lu: p-Cycle design in survivable WDM networks with shared risk link groups (SRLGs). Photonic Netw. Commun.
**11**, 301–311 (2006)CrossRefGoogle Scholar - 47.Zhang, Qingfu, Sun, Jianyong, Xiao, Gaoxi, Tsang, Edward: Evolutionary algorithms refining a heuristic: a hybrid method for shared-path protections in WDM networks under SRLG constraints. IEEE Trans. Syst. Man Cybern. Part B Cybern.
**37**(1), 51–61 (2007)zbMATHCrossRefGoogle Scholar - 48.Bermond, J.-C., Coudert, D., D’Angelo, G., Moataz, F.Z.: SRLG-diverse routing with the star property. In: Proceedings of the 9th International Conference on the Design of Reliable Communication Networks, DRCN 2013, pp. 163–170. IEEE, 4–7 March 2013Google Scholar