Approximating the Diameter of Planar Graphs in Near Linear Time

TL;DR

This paper introduces a near-linear time algorithm that approximates the diameter of undirected planar graphs with non-negative edge lengths within a factor of (1+ε), significantly improving efficiency over previous methods.

Contribution

The paper presents the first near-linear time approximation algorithm for the graph diameter problem in planar graphs, with a tunable approximation factor.

Findings

Achieves (1+ε)-approximation in O(f(ε)·n log^4 n) time

Significantly faster than exact algorithms for large graphs

Applicable to large-scale planar network analysis

Abstract

We present a $(1+\epsilon)$-approximation algorithm running in $O(f(\epsilon)\cdot n \log^4 n)$ time for finding the diameter of an undirected planar graph with non-negative edge lengths.