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Network survivability is very important due to the growth of Internet traffic and the number of services/business depending on telecommunication networks. A Shared Risk Link Group (SRLG) is the set of links in the network that share a common physical resource subject to fault(s). The fault of a given network resource implies a fault in all links in the corresponding SRLG. The concept of SRLG allows an upper layer to be able to implement SRLG diverse routing, that is to calculate, for a given Active Path (AP), a Backup Path (BP), which avoids every SRLG that may involve the selected AP. Firstly we will present a short revision of the Conflicting SRLG Exclusion (CoSE) and of the Iterative Modified Suurballe's Heuristic (IMSH). The CoSE algorithm solves the minmin problem extending the Conflicting Link Exclusion (COLE) algorithm by replacing the calculation of the conflicting link set by the calculation of the conflicting SRLG set. Secondly we will propose a new version of CoSE, which we designate as CoSE-MS, for solving the min-sum problem. This is achieved by introducing a modified Bhandari's edge-disjoint shortest path pair heuristic (MBH) and using the Modified Suurballe's Heuristic (MSH) in the original version of CoSE. Thirdly we will compare CoSE-MS performance with IMSH.