The Edge-Disjoint Path Problem on Random Graphs by Message-Passing
Fig 1
An instance of the MWEDP problem over a 3-regular random graph of V = 20 and M = 6: examples of solutions of the unconstrained (left) and optimal (right) MWEDP problem are displayed.
In the latter, the purple communication is redirected along a longer path to avoid edge-overlap. The yellow one has two shortest paths of equal length (degeneracy) in the unconstrained case, but once the edge-disjointness is enforced this degeneracy is broken and only one of the two is optimal (right).