The Undirected Two Disjoint Shortest Paths Problem
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The k disjoint shortest paths problem (k-DSPP) on a graph with k source-sink pairs (s_i, t_i) asks for the existence of k pairwise edge- or vertex-disjoint shortest s_i-t_i-paths. It is known to be NP-complete if k is part of the input. Restricting to 2-DSPP with strictly positive lengths, it becomes solvable in polynomial time. We extend this result by allowing zero edge lengths and give a polynomial time algorithm based on dynamic programming for 2-DSPP on undirected graphs with non-negative edge lengths.
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