Geodesic diameter of a polygonal domain in O(n^4 log n) time

TL;DR

This paper presents an algorithm to compute the geodesic diameter of a polygonal domain with n vertices efficiently in O(n^4 log n) time by analyzing candidate endpoints derived from shortest path maps.

Contribution

The paper introduces a novel method to compute the geodesic diameter in polygonal domains using a new candidate endpoint approach with improved complexity.

Findings

Achieves O(n^4 log n) time complexity for the diameter computation.

Identifies a set of O(n^3) candidate endpoints for the diameter.

Utilizes shortest path maps to determine candidate endpoints efficiently.

Abstract

We show that the geodesic diameter of a polygonal domain with n vertices can be computed in O(n^4 log n) time by considering O(n^3) candidate diameter endpoints; the endpoints are a subset of vertices of the overlay of shortest path maps from vertices of the domain.