Online and Offline Learning of Orderly Hypergraphs Using Queries

Shaun Fallat, Kamyar Khodamoradi, David G. Kirkpatrick, Valerii Maliuk, Seyed Ahmad Mojallal, Sandra Zilles

Keywords: Learning hypergraphs, shortest-path queries, online algorithms, hypergraph acyclicity

Abstract:

In the context of learning hypergraphs with shortest-path queries (SP-queries), we present the first provably optimal online algorithm for learning a broad and natural class of hypertrees which we call orderly hypertrees. Our online algorithm can be transformed into a provably optimal offline algorithm.
Orderly hypertrees can be positioned within the Fagin hierarchy of hypergraph acyclicity (studied in database theory), and strictly encompass the broadest class in this hierarchy that is learnable with subquadratic SP-query complexity.
Our results also motivate the study of a new type of query, called dependency query (D-query), which is weaker than an SP-query. Positive and negative results on D-queries shed light on the structural properties of classes of hypertrees for which efficient learning requires the full information provided by SP-queries.

Submission Number: 78