a method is given for deriving a backup path routing spare capacity template that is feasible , scalable , adaptive , much faster , and near global optimal in redundancy reduction . the method includes determining working paths , aggregating the working paths into a first matrix , determining backup paths , aggregating the backup paths into a second matrix , and deriving the template from the first and second matrices . a method is also given for successively approximating the optimal spare capacity allocation needed for a network . the method includes , determining the link cost associated with a selected traffic flow &# 39 ; s backup path , determining an updated link cost that is less than the current link cost , determining a backup path with the updated link cost , and notifying the rest of the network of the backup path .