Hierarchical Exponential Search Via K-Spines

TL;DR

This paper presents a novel hierarchical exponential search algorithm on trees using the concept of k-spines, which are paths that help efficiently locate targets by focusing search along these central paths.

Contribution

The paper introduces the concept of k-spines and develops an O(k log dist) exponential search algorithm that leverages these structures for efficient tree searches.

Findings

Efficient search algorithm with O(k log dist) complexity.

Introduction of the k-spine concept for tree decomposition.

Improved search performance by focusing on central paths.

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.