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Due to the computational complexity of finding almost shortest simple paths,we propose that identifying a larger collection of (nonbacktracking) paths ismore efficient than finding almost shortest simple paths on positively weightedreal-world networks. First, we present an easy to implement $O(m\log m+kL)$solution for finding all (nonbacktracking) paths with bounded length $D$between two arbitrary nodes on a positively weighted graph, where $L$ is anupperbound for the number of nodes in any of the $k$ outputted paths.Subsequently, we illustrate that for undirected Chung-Lu random graphs, theratio between the number of nonbacktracking and simple paths asymptoticallyapproaches $1$ with high probability for a wide range of parameters. We thenconsider an application to the almost shortest paths algorithm to measure pathdiversity for internet routing in a snapshot of the Autonomous System graphsubject to an edge deletion process.

The K Shortest Paths Problem with Application to Routing