Factorization of products of hypergraphs: Structure and algorithms

On the one hand Cartesian products of graphs have been extensively studied since the 1960s. On the other hand hypergraphs are a well-known and useful generalization of graphs. In this article, we present an algorithm able to factorize into its prime factors any bounded-rank and bounded-degree hypergraph in O(nm), where n is the number of vertices and m is the number of hyperedges of the hypergraph. First the algorithm applies a graph factorization algorithm to the 2-section of the hypergraph. Then the 2-section factorization is used to build the factorization of the hypergraph via the factorization of its L2-section. The L2-section is a recently introduced way to interpret a hypergraph as a labeled-graph. The graph factorization algorithm used in this article is due to Imrich and Peterin and is linear in time and space. Nevertheless any other such algorithm could be extended to a hypergraph factorization algorithm similar to the one presented here.

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