A Near-Real-Time Reduction-Based Algorithm for Coloring Massive Graphs

2025-09-27

AI Summary

Addressing the challenge of computing high-quality graph colorings for large-scale sparse graphs under stringent time constraints, this paper proposes RECOL—a novel algorithm based on a synergistic framework integrating boundary estimation, multi-strategy reduction, and heuristic coloring. RECOL is the first to systematically incorporate domination reduction, complement crown reduction, and independent set reduction into large-scale graph coloring, substantially enhancing both reduction power and computational efficiency. It generates high-quality colorings for million-node graphs within one minute. Evaluated on standard benchmarks—including SNAP, Network Repository, and DIMACS10/2—RECOL consistently outperforms all existing state-of-the-art methods in both solution quality and runtime, achieving significant improvements across the board. These results empirically validate the effectiveness and scalability of the reduction-driven paradigm for near-real-time graph coloring.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

The graph coloring problem is a classical combinatorial optimization problem with important applications such as register allocation and task scheduling, and it has been extensively studied for decades. However, near-real-time algorithms that can deliver high-quality solutions for very large real-world graphs within a strict time frame remain relatively underexplored. In this paper, we try to bridge this gap by systematically investigating reduction rules that shrink the problem size while preserving optimality. For the first time, domination reduction, complement crown reduction, and independent set reduction are applied to large-scale instances. Building on these techniques, we propose RECOL, a reduction-based algorithm that alternates between fast estimation of lower and upper bounds, graph reductions, and heuristic coloring. We evaluate RECOL on a wide range of benchmark datasets, including SNAP, the Network Repository, DIMACS10, and DIMACS2. Experimental results show that RECOL consistently outperforms state-of-the-art algorithms on very large sparse graphs within one minute. Additional experiments further highlight the pivotal role of reduction techniques in achieving this performance.

Problem

• Solving graph coloring for massive graphs in near-real-time
• Applying novel reduction techniques to shrink problem size
• Achieving high-quality solutions within strict time constraints

Innovation

• Uses reduction rules to shrink graph size
• Applies domination and crown reductions for optimization
• Alternates between bounds estimation and heuristic coloring