Enumerating $k$-arc-connected orientations

Sarah Blind (1) , Kolja Knauer (2, 3) , Petru Valicov (4, 3)

1 LGIPM - Laboratoire de Génie Informatique, de Production et de Maintenance
2 UB - Universitat de Barcelona
3 ACRO - Algorithmique, Combinatoire et Recherche Opérationnelle
4 ALGCO - Algorithmes, Graphes et Combinatoire

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.

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Sarah Blind, Kolja Knauer, Petru Valicov. Enumerating $k$-arc-connected orientations. Algorithmica, 2020, 82 (12), ⟨10.1007/s00453-020-00738-y⟩. ⟨hal-02435175v2⟩