English

Optimal bounds on a tree inference algorithm

Data Structures and Algorithms 2024-12-05 v1

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-kk tree of nn leaves is O(nklogkn)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(nklogkn)O(n k \log_k n) algorithm.

Keywords

Cite

@article{arxiv.2412.03138,
  title  = {Optimal bounds on a tree inference algorithm},
  author = {Jack Gardiner and Lachlan L. H. Andrew and Junhao Gan and Jean Honorio and Seeun William Umboh},
  journal= {arXiv preprint arXiv:2412.03138},
  year   = {2024}
}