We study the problem of reconstructing a hidden graph, which can only be accessed by querying pairs of vertices and getting their shortest path or their distance in the graph. We wish to design algorithms with small query complexity. We also study approximate reconstruction.
Further, we explore the verification problem, in which we are given a hypothetical graph and wish to verify that the graph is correct using few queries.
We make progress on those problems for graphs of bounded degree, outerplanar graphs, and graphs of bounded treewidth.
(Joint work with Claire Mathieu and partly with Sampath Kannan)