Finding long simple paths in a weighted digraph using pseudo-topological orderings

TL;DR

This paper introduces a heuristic algorithm combining DFS and pseudo-topological orderings to find long simple paths in weighted digraphs, addressing an NP-hard problem with practical effectiveness demonstrated by a competition win.

Contribution

It presents a novel hybrid heuristic algorithm using pseudo-topological orderings and edge opening, advancing methods for tackling NP-hard longest path problems in graphs.

Findings

Algorithm won Oracle MDC 2015 coding competition

Efficient heuristic for long simple paths in weighted digraphs

Generalizes topological orderings to non-acyclic graphs

Abstract

Given a weighted digraph D, finding the longest simple path is well known to be NP-hard. Furthermore, even giving an approximation algorithm is known to be NP-hard. In this paper we describe an efficient heuristic algorithm for finding long simple paths, using an hybrid approach of DFS and pseudo-topological orders, a a generalization of topological orders to non acyclic graphs, via a process we call "opening edges". An implementation of this algorithm won the Oracle MDC 2015 coding competition.