Exact Learning of Multitrees and Almost-Trees Using Path Queries

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 ∈ 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.