Hyper-distance oracles in hypergraphs

We study point-to-point distance estimation in hypergraphs, where the query is parameterized by a positive integer s , which defines the required level of overlap for two hyperedges to be considered adjacent. To answer s -distance queries, we first explore an oracle based on the line graph of the given hypergraph and discuss its limitations: The line graph is typically orders of magnitude larger than the original hypergraph. We then introduce HypED , a landmark-based oracle with a predefined size, built directly on the hypergraph, thus avoiding the materialization of the line graph. Our framework allows to approximately answer vertex-to-vertex, vertex-to-hyperedge, and hyperedge-to-hyperedge s -distance queries for any value of s . A key observation at the basis of our framework is that as s increases, the hypergraph becomes more fragmented. We show how this can be exploited to improve the placement of landmarks, by identifying the s -connected components of the hypergraph. For this latter task, we devise an efficient algorithm based on the union-find technique and a dynamic inverted index. We experimentally evaluate HypED on several real-world hypergraphs and prove its versatility in answering s -distance queries for different values of s . Our framework allows answering such queries in fractions of a millisecond while allowing fine-grained control of the trade-off between index size and approximation error at creation time. Finally, we prove the usefulness of the s -distance oracle in two applications, namely hypergraph-based recommendation and the approximation of the s -closeness centrality of vertices and hyperedges in the context of protein-protein interactions.