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The Cartographer
Optimal bounds on a tree inference algorithm
December 04, 2024 Β· Declared Dead Β· π arXiv.org
"No code URL or promise found in abstract"
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Authors
Jack Gardiner, Lachlan L. H. Andrew, Junhao Gan, Jean Honorio, Seeun William Umboh
arXiv ID
2412.03138
Category
cs.DS: Data Structures & Algorithms
Citations
0
Venue
arXiv.org
Last Checked
5 months ago
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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