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Motivated from parallel network mapping, we provide efficient query complexity and round complexity bounds for graph reconstruction using distance queries, including a bound that improves a previous sequential complexity bound. Our methods use a highprobability parametric parallelization of a graph clustering technique of Thorup and Zwick, which may be of independent interest.

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.

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