Reduction Rules and ILP Are All You Need: Minimal Directed Feedback Vertex Set

TL;DR

This paper presents an exact solver for the Minimal Directed Feedback Vertex Set problem that combines reduction rules from Vertex Cover literature with ILP solving, achieving strong performance in a competitive setting.

Contribution

The paper introduces a novel approach that reduces the DFVS problem to a Cover problem and applies ILP, including a new vertex cover reduction generalizing the Desk rule.

Findings

Solver achieved second-best performance in PACE 2022

Reduction rules significantly simplify the problem

ILP approach effectively solves the reduced instances

Abstract

This note describes the development of an exact solver for Minimal Directed Feedback Vertex Set as part of the PACE 2022 competition. The solver is powered largely by aggressively trying to reduce the DFVS problem to a Minimal Cover problem, and applying reduction rules adapted from Vertex Cover literature. The resulting problem is solved as an Integer Linear Program (ILP) using SCIP. The resulting solver performed the second-best in the competition, although a bug at submission time disqualified it. As an additional note, we describe a new vertex cover reduction generalizing the Desk reduction rule.