# 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.

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