An efficient implementation for solving the all pairs minimax path problem in an undirected dense graph

TL;DR

This paper presents an efficient $O(n^2)$ implementation for the all pairs minimax path problem in undirected dense graphs, demonstrating significant performance improvements over existing methods through experiments.

Contribution

It provides the first practical code implementation of Algorithm 4 for solving the APPD matrix in $O(n^2)$, validating its efficiency and accuracy.

Findings

Algorithm 4 outperforms other algorithms in experiments.

The implementation drastically improves APPD matrix computation efficiency.

Theoretical $O(n^2)$ solutions are impractical without code; this work provides one.

Abstract

We provide an efficient $ O(n^2) $ implementation for solving the all pairs minimax path problem or widest path problem in an undirected dense graph. It is a code implementation of the Algorithm 4 (MMJ distance by Calculation and Copy) in a previous paper. The distance matrix is also called the all points path distance (APPD). We conducted experiments to test the implementation and algorithm, compared it with several other algorithms for solving the APPD matrix. Result shows Algorithm 4 works good for solving the widest path or minimax path APPD matrix. It can drastically improve the efficiency for computing the APPD matrix. There are several theoretical outcomes which claim the APPD matrix can be solved accurately in $ O(n^2) $ . However, they are impractical because there is no code implementation of these algorithms. It seems Algorithm 4 is the first algorithm that has an actual code implementation for solving the APPD matrix of minimax path or widest path problem in $ O(n^2) $, in an undirected dense graph.