Polynomial Delay and Space Discovery of Connected and Acyclic Sub-hypergraphs in a Hypergraph

In this paper, we study the problem of finding all connected and Berge-acyclic sub-hypergraphs contained in an input hypergraph with potential applications to substructure mining from relational data, where Berge acyclicity is a generalization of a tree and one of the most retricted notion of acyclicity for hypergraphs (Fagin, J. ACM, Vol.30(3), pp.514–550, 1983). As main results, we present efficient depth-first algorithm that finds all connected and Berge acyclic sub-hypergraphs S contained in an input hypergraph H with m hyperedges and n vertices in O(nm) delay (time per solution) using O(N) space, where N = ||H|| is the total input size. In the algorithms, we use maximum elimination sequences. This result gives the first polynomial delay and time algorithm for discovery of Berge-acyclic sub-hypergraphs. We also discuss adaptive enumeration whose delay depends only on a parameter on each discovered subgraph S, rather than the whole input of size N . Our modified algorithm runs in O(k + k′) delay using O(N) space and preprocessing, where its delay depends only on the size k = ||S|| of a sub-hypergraph S to find and the size k′ = ||N(S)|| of its neighbor hyperedges.