The Feedback Arc Set Problem with Triangle Inequality is a Vertex Cover Problem

TL;DR

This paper reveals that the Feedback Arc Set problem with triangle inequality constraints can be viewed as a vertex cover problem in hypergraphs, enabling new approximation algorithms and insights.

Contribution

It establishes a structural equivalence between the Feedback Arc Set problem with triangle inequalities and a hypergraph vertex cover problem, facilitating novel algorithmic approaches.

Findings

The problem is a special case of minimum vertex cover in hypergraphs of size at most 3.

Structural insight enables combinatorial approximation algorithms.

Links Feedback Arc Set with hypergraph vertex cover, broadening research avenues.

Abstract

We consider the (precedence constrained) Minimum Feedback Arc Set problem with triangle inequalities on the weights, which finds important applications in problems of ranking with inconsistent information. We present a surprising structural insight showing that the problem is a special case of the minimum vertex cover in hypergraphs with edges of size at most 3. This result leads to combinatorial approximation algorithms for the problem and opens the road to studying the problem as a vertex cover problem.