Optimal Longest Paths by Dynamic Programming

TL;DR

This paper introduces an optimal dynamic programming algorithm for the longest path problem in undirected weighted graphs, significantly improving speed and enabling solutions to previously unsolvable instances.

Contribution

The paper presents a novel dynamic programming approach combined with graph partitioning that outperforms existing methods for the longest path problem.

Findings

Algorithm is significantly faster than previous methods

Enables solving larger and more complex instances

Outperforms state-of-the-art algorithms in benchmarks

Abstract

We propose an optimal algorithm for solving the longest path problem in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster than other state-of-the-art methods. This enables us to solve instances that have previously been unsolved.