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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
A Near-Real-Time Reduction-Based Algorithm for Coloring M...
Chenghao Zhu, Yi Zhou · 2025-09-28 · via cs.DS updates on arXiv.org

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.