{"ID":2850147,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.22837","arxiv_id":"2510.22837","title":"Hierarchical Exponential Search Via K-Spines","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.","short_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 dow...","url_abs":"https://arxiv.org/abs/2510.22837","url_pdf":"https://arxiv.org/pdf/2510.22837v2","authors":"[\"Bob Dong\"]","published":"2025-10-26T21:08:27Z","proceeding":"cs.DS","tasks":"[\"cs.DS\"]","methods":"[]","has_code":false}