Enumerating \(k\)-arc-connected orientations

We study the problem of enumerating the \(k\)-arc-connected orientations of a graph \(G\), i.e., generating each exactly once. A first algorithm using submodular flow optimization is easy to state, but intricate to implement. In a second approach we present a simple algorithm with \(O(knm^2)\) time delay and amortized time \(O(m^2)\), which improves over the analysis of the submodular flow algorithm. As ingredients, we obtain enumeration algorithms for the \(\alpha\)-orientations of a graph \(G\) in \(O(m^2)\) time delay and for the outdegree sequences attained by \(k\)-arc-connected orientations of \(G\) in \(O(knm^2)\) time delay.