A method implemented by a source router reduces the number of SPF computations needed to compute TI-LFA backup paths. Rather than naively perform a backup path computation for all destinations, the source router identifies those destinations affected by that link or node failure and performs backup path computations only for the affected destinations. For the remaining destinations (i.e., those for which a backup path is required), the backup path computations are performed in a breath-first order relative to a subtree rooted at the node incident to the failed link (in the case of a link failure) or at the protected node (in the case of a node failure). The breath-first order further reduces the number of computations required by taking advantage of earlier backup path computations.