Finding Optimal Longest Paths by Dynamic Programming in Parallel

TL;DR

This paper introduces a new exact algorithm for the longest simple path problem that leverages graph partitioning and dynamic programming, achieving faster solutions and scalable parallelization for previously intractable instances.

Contribution

It presents the first efficient parallel algorithm for the longest simple path problem, significantly improving solution speed and scalability over existing methods.

Findings

Faster solution times compared to state-of-the-art methods

Ability to solve previously unsolvable instances

First scalable parallel algorithm for the problem

Abstract

We propose an exact algorithm for solving the longest simple path problem between two given vertices 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 were previously unsolved and solve hard instances significantly faster. Lastly, we present a scalable parallelization which yields the first efficient parallel algorithm for the problem.