Fast Dynamic Pointer Following via Link-Cut Trees

TL;DR

This paper introduces an efficient data structure based on link-cut trees for dynamic pointer following in graphs with outdegree one, supporting updates and queries in logarithmic time, proven optimal in the cell-probe model.

Contribution

The paper presents a novel $O( ext{log } n)$ solution for dynamic pointer following using link-cut trees, establishing optimality in the cell-probe model.

Findings

Supports edge updates and pointer queries in $O( ext{log } n)$ time.

Proves the optimality of the solution in the cell-probe complexity model.

Provides a theoretical foundation for efficient dynamic graph traversal operations.

Abstract

In this paper, we study the problem of fast dynamic pointer following: given a directed graph $G$ where each vertex has outdegree $1$, efficiently support the operations of i) changing the outgoing edge of any vertex, and ii) find the vertex $k$ vertices `after' a given vertex. We exhibit a solution to this problem based on link-cut trees that requires $O(\lg n)$ time per operation, and prove that this is optimal in the cell-probe complexity model.