Node Adjacency In Hypergraphs

We present an algorithm for answering adjacency queries or building an adjacency matrix in a hypergraph. The algorithm exhibits a logarithmic speed-up compared to a naive method of examining all hyperedges. In a hypergraph with n nodes, m hyperedges and sum of hyperedge sizes M, it answers individual adjacency queries in O(m/log m), with a O(M + m(1+epsilon)/log m) preprocessing time. It represents a new approach based on equivalence classes of nodes. The results are also applicable to detecting witnesses in Boolean matrix products.