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arXiv · 2511.22014

Distance-based Learning of Hypertrees

Shaun Fallat·Kamyar Khodamoradi·David Kirkpatrick·Valerii Maliuk·S. Ahmad Mojallal·Sandra Zilles
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Abstract

We study the problem of learning hypergraphs with shortest-path queries (SP-queries), and present the first provably optimal online algorithm for a broad and natural class of hypertrees that 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 acyclic hypergraph (well-studied in database theory), and strictly encompass the broadest class in this hierarchy that is learnable with subquadratic SP-query complexity. Recognizing that in some contexts, such as evolutionary tree reconstruction, distance measurements can degrade with increased distance, we also consider a learning model that uses bounded distance queries. In this model, we demonstrate asymptotically tight complexity bounds for learning general hypertrees.

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Shaun Fallat, Kamyar Khodamoradi, David Kirkpatrick, Valerii Maliuk, S. Ahmad Mojallal, Sandra Zilles. 2025-11-27. Distance-based Learning of Hypertrees. https://arxiv.org/abs/2511.22014

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