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arXiv · 2510.22837

Hierarchical Exponential Search Via K-Spines

Bob Dong
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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.

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Bob Dong. 2025-10-26. Hierarchical Exponential Search Via K-Spines. https://arxiv.org/abs/2510.22837

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