An average study of hypergraphs and their minimal transversals

In this paper, we study some average properties of hypergraphs and the average complexity of algorithms applied to hypergraphs under different probabilistic models. Our approach is both theoretical and experimental since our goal is to obtain a random model that is able to capture the real-data complexity. Starting from a model that generalizes the Erdös-Renyi model [9, 10], we obtain asymptotic estimations on the average number of transversals, minimals and minimal transversals in a random hypergraph. We use those results to obtain an upper bound on the average complexity of algorithms to generate the minimal transversals of an hypergraph. Then we make our random model more complex in order bring it closer to real-data and identify cases where the average number of minimal tranversals is at most polynomial, quasipolynomial or exponential.