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arXiv · 2603.10432

Reconstructing Bounded Treelength Graphs with Linearithmic Shortest Path Distance Queries

Chirag Kaudan·Amir Nayyeri
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Abstract

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 $u,v \in V$ and returns the shortest path distance between $u$ and $v$, how many queries are needed to reconstruct $E$? Specifically, we consider bounded degree $\Delta$ and bounded treelength $\mathrm{tl}$ connected graphs and show that reconstruction can be done in $O_{\Delta,\mathrm{tl}}(n \log n)$ 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.

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Chirag Kaudan, Amir Nayyeri. 2026-03-11. Reconstructing Bounded Treelength Graphs with Linearithmic Shortest Path Distance Queries. https://arxiv.org/abs/2603.10432

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