On Learning a Hidden Directed Graph with Path Queries

TL;DR

This paper investigates algorithms for reconstructing hidden directed graphs using path queries, providing bounds, new algorithms for special graph classes, and lower bounds to justify their methods.

Contribution

It introduces new bounds and algorithms for learning directed graphs, especially bounded degree trees and almost-trees, with theoretical justifications.

Findings

Bounds for learning graphs with $n$ vertices and $k$ strongly connected components.

New algorithms for learning almost-trees with added edges.

Lower bounds supporting the proposed algorithms.

Abstract

In this paper, we consider the problem of reconstructing a directed graph using path queries. In this query model of learning, a graph is hidden from the learner, and the learner can access information about it with path queries. For a source and destination node, a path query returns whether there is a directed path from the source to the destination node in the hidden graph. In this paper we first give bounds for learning graphs on $n$ vertices and $k$ strongly connected components. We then study the case of bounded degree directed trees and give new algorithms for learning "almost-trees" -- directed trees to which extra edges have been added. We also give some lower bound constructions justifying our approach.