An $O(n\log n)$ Algorithm for Single-Source Shortest Paths in Disk Graphs

TL;DR

This paper presents an efficient algorithm for solving the single-source shortest-path problem in disk graphs with a time complexity of O(n log n), and extends the approach to intersection graphs of fat triangles with O(n log^2 n).

Contribution

The paper introduces a novel O(n log n) algorithm for shortest paths in disk graphs and extends it to fat triangle intersection graphs, improving computational efficiency.

Findings

Single-source shortest paths in disk graphs can be solved in O(n log n) time.

Extension to fat triangle intersection graphs achieved in O(n log^2 n) time.

Provides theoretical bounds and algorithms for geometric graph shortest path problems.

Abstract

We prove that the single-source shortest-path problem on disk graphs can be solved in $O(n\log n)$ time, and that it can be solved on intersection graphs of fat triangles in $O(n\log^2 n)$ time.