We consider the following graph reconstruction problem: given an unweighted connected graph G = (V,E) with visible vertex set V and an oracle which takes two vertices u,v ∈ V and returns the shortest path distance between u and v, how many queries are needed to reconstruct E? Specifically, we consider bounded degree Δ and bounded treelength tl connected graphs and show that reconstruction can be done in O_Δ,tl(n log n) queries with a deterministic algorithm. This result improves over the best known algorithm (deterministic or randomized) for this graph class by a log n factor and matches the known lower bound for the class of graphs with bounded chordality, which is a subclass of bounded treelength graphs.
