I was reading about Suurballe's algorithm on Wikipedia, for the shortestedge-disjoint paths problem, i.e. given nodes $s$ and $t$ finding a pair of paths between these nodes, whose accumulated weight is minimal.I understand why the output consists of two $s$-$t$ paths, and the relationship between this and augmenting path flow algorithms on an intuitive level, however I fail to understand why the two paths the algorithm chooses necessarily minimize the weight.I would appreciate if somebody could explain why the algorithm is correct. I don't have access to Suurballe's original paper and I can't follow the paper by Suurballe and Tarjan.
Suurballe's Algorithm: Proof of Correctness
algorithms;graphs;shortest path;correctness proof