  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 main one is that 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 constructing 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 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 hyper-edges in the context of protein-to-protein
interactions.
