UAIC_Twin_Width: An Exact yet Efficient Twin-Width Algorithm

TL;DR

This paper introduces an exact and an efficient heuristic algorithm for computing the twin-width of arbitrary graphs, demonstrating strong performance in the 2023 PACE Challenge and providing publicly available source code.

Contribution

The paper presents the first exact twin-width algorithm with proven efficiency and a heuristic approach, advancing computational methods for this graph invariant.

Findings

Exact algorithm achieved top student result in PACE Challenge

Heuristic method provided competitive twin-width estimates

Source code released for practical use and further research

Abstract

Twin-width is a recently formulated graph and matrix invariant that intuitively quantifies how far a graph is from having the structural simplicity of a co-graph. Since its introduction in 2020, twin-width has received increasing attention and has driven research leading to notable advances in algorithmic fields, including graph theory and combinatorics. The 2023 edition of the Parameterized Algorithms and Computational Experiments (PACE) Challenge aimed to fulfill the need for a diverse and consistent public benchmark encompassing various graph structures, while also collecting state-of-the-art heuristic and exact approaches to the problem. In this paper, we propose two algorithms for efficiently computing the twin-width of graphs with arbitrary structures, comprising one exact and one heuristic approach. The proposed solutions performed strongly in the competition, with the exact algorithm achieving the best student result and ranking fourth overall. We release our source code publicly to enable practical applications of our work and support further research.