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

Gangli Liu

TL;DR: We present the fastest algorithm for solving the all-pairs minimax path problem or widest path problem matrix by far, in undirected dense graphs.

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. 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. 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.

Primary Area: Theory->Optimization

Keywords: Minimax path problem, Longest-leg path distance, Min-Max-Jump distance, Widest path problem, Maximum capacity path problem, Bottleneck edge query problem, All points path distance, Floyd-Warshall algorithm;, Minimum spanning tree

Submission Number: 10907