Hierarchical Exponential Search Via K-Spines
Data Structures and Algorithms
2025-10-29 v2
Abstract
We introduce the concept of a k-spine of a tree. A k-spine is essentially a path in the tree whose removal leaves only "less-bushy" components of a smaller pathwidth. Using a k-spine as a central guide, we introduce an O(klog dist) exponential search algorithm on a tree by searching mainly along the spine to narrow down the target's vicinity and then recursively handling the smaller components.
Keywords
Cite
@article{arxiv.2510.22837,
title = {Hierarchical Exponential Search Via K-Spines},
author = {Bob Dong},
journal= {arXiv preprint arXiv:2510.22837},
year = {2025}
}
Comments
This was an unintentional early upload of a work-in-progress draft from an ongoing collaboration. The posting was premature and not meant for public release