Exact Learning of Multitrees and Almost-Trees Using Path Queries

TL;DR

This paper investigates the problem of exactly learning specific classes of directed graphs, such as multitrees and almost-trees, using path queries, providing algorithms and lower bounds for the query complexity involved.

Contribution

It introduces efficient algorithms and establishes lower bounds for the query complexity of exactly learning multitrees and almost-trees with path queries.

Findings

Provided algorithms for learning multitrees and almost-trees.

Established lower bounds on the number of queries needed.

Applied results to butterfly networks.

Abstract

Given a directed graph, G=(V,E), a path query, path(u,v), returns whether there is a directed path from u to v in G, for u,v vertices in V. Given only V, exactly learning all the edges in G using path queries is often impossible, since path queries cannot detect transitive edges. In this paper, we study the query complexity of exact learning for cases when learning G is possible using path queries. In particular, we provide efficient learning algorithms, as well as lower bounds, for multitrees and almost-trees, including butterfly networks.