Succinct data-structure for nearest colored node in a tree

TL;DR

This paper introduces a space-efficient data structure for quickly finding the nearest node of a specific color in a tree, improving upon previous methods in terms of storage size.

Contribution

The authors present a succinct data structure that reduces space complexity while maintaining efficient nearest-colored node queries in trees.

Findings

Reduces space from previous $O(n ext{log}n)$ bits to a more succinct form.

Supports fast nearest-colored node queries in trees.

Improves theoretical bounds for colored node queries in trees.

Abstract

We give a succinct data-structure that stores a tree with colors on the nodes. Given a node x and a color alpha, the structure finds the nearest node to x with color alpha. This results improves the $O(n\log n)$-bits structure of Gawrychowski et al.~[CPM 2016].