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arXiv · 2412.03138

Optimal bounds on a tree inference algorithm

Jack Gardiner·Lachlan L. H. Andrew·Junhao Gan·Jean Honorio·Seeun William Umboh
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Abstract

This paper tightens the best known analysis of Hein's 1989 algorithm to infer the topology of a weighted tree based on the lengths of paths between its leaves. It shows that the number of length queries required for a degree-$k$ tree of $n$ leaves is $O(n k \log_k n)$, which is the lower bound. It also presents a family of trees for which the performance is asymptotically better, and shows that no such family exists for a competing $O(n k \log_k n)$ algorithm.

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Jack Gardiner, Lachlan L. H. Andrew, Junhao Gan, Jean Honorio, Seeun William Umboh. 2024-12-04. Optimal bounds on a tree inference algorithm. https://arxiv.org/abs/2412.03138

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