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PreprintCC BY 4.0arXiv

A Crawling Metric on the Space of Subtrees of a Tree

  • Thu-Le Tran
  • Cao Minh Quang
  • Nguyen Chi Tam
  • Kien Trung Nguyen
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Abstract

We propose a crawling metric on the space of subtrees of a tree. The symmetric difference cannot tell whether two disjoint subtrees are close or far; we halve it and add the gap between them. The result is a metric, one half is the smallest factor, and the tree embeds canonically. The metric equals the least cost of crawling between subtrees by growing and shrinking without jumping. With simultaneous growth and shrinkage, subtrees of fixed length form a geodesic space.

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Cite

BibTeXRIS
BibTeX
@misc{tran2026crawling,
  title = {{A Crawling Metric on the Space of Subtrees of a Tree}},
  author = {Thu-Le Tran and Cao Minh Quang and Nguyen Chi Tam and Kien Trung Nguyen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24448},
  eprint = {2610.24448},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24448},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Crawling Metric on the Space of Subtrees of a Tree
AU  - Thu-Le Tran
AU  - Cao Minh Quang
AU  - Nguyen Chi Tam
AU  - Kien Trung Nguyen
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24448
UR  - https://arxiv.org/abs/2610.24448
AB  - We propose a crawling metric on the space of subtrees of a tree. The symmetric difference cannot tell whether two disjoint subtrees are close or far; we halve it and add the gap between them. The result is a metric, one half is the smallest factor, and the tree embeds canonically. The metric equals the least cost of crawling between subtrees by growing and shrinking without jumping. With simultaneous growth and shrinkage, subtrees of fixed length form a geodesic space.
ER  -