For random nearest neighbor trees, the root can be found among a confidence set of size roughly log(1/epsilon) divided by log log(1/epsilon) in one dimension.
Root finding algorithms and persistence of Jordan centrality in growing random trees
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Finding the root in random nearest neighbor trees
For random nearest neighbor trees, the root can be found among a confidence set of size roughly log(1/epsilon) divided by log log(1/epsilon) in one dimension.