Graph Reconstruction via Distance Oracles

TL;DR

This paper introduces randomized algorithms for reconstructing various classes of graphs using distance oracles, achieving improved query complexities for degree-bounded and outerplanar graphs, and near-optimal results for general graphs.

Contribution

It presents new randomized algorithms for graph reconstruction with optimized query complexities for specific graph classes.

Findings

Reconstruction of degree-bounded graphs with  O(n^{3/2}) queries.

Reconstruction of outerplanar graphs with  O(n) queries.

Near-optimal approximate reconstruction of general graphs.

Abstract

We study the problem of reconstructing a hidden graph given access to a distance oracle. We design randomized algorithms for the following problems: reconstruction of a degree bounded graph with query complexity $\tilde{O}(n^{3/2})$; reconstruction of a degree bounded outerplanar graph with query complexity $\tilde{O}(n)$; and near-optimal approximate reconstruction of a general graph.