UAIC_Twin_Width: An Exact yet Efficient Twin-Width Algorithm

2025-11-09

AI Summary

This work addresses the exact computation of twin-width—a recently introduced graph parameter quantifying structural complexity. We propose the first general-purpose algorithmic framework that balances computational efficiency with solution accuracy. Methodologically, our approach integrates graph reduction rules, heuristic search optimization, and branch-and-bound techniques to simultaneously deliver exact solutions and high-quality approximate results. In the PACE 2023 international algorithm implementation challenge, our exact solver won the Best Student Team Award and ranked fourth overall globally. All source code is publicly released, facilitating standardization and empirical research on twin-width. To our knowledge, this is the first work to elevate twin-width computation from theoretical construction to a scalable, reproducible, and practical tool. It substantially advances the feasibility and performance limits of parameterized graph algorithms on real-world complex networks.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Developing efficient algorithms to compute graph twin-width invariant
• Addressing the need for diverse public benchmark of graph structures
• Providing exact and heuristic approaches for arbitrary graph structures

Innovation

• Exact algorithm for computing twin-width
• Heuristic approach for graph twin-width
• Public source code for practical applications