Unrealized Expectations: Comparing AI Methods vs Classical Algorithms for Maximum Independent Set

2025-02-05

AI Summary

This work systematically evaluates the practical performance of AI-based approaches—specifically GFlowNet-LTFT and reinforcement learning—against classical algorithms (e.g., KaMIS) for the Maximum Independent Set (MIS) problem. Experiments across diverse synthetic and benchmark graphs reveal that state-of-the-art GPU-accelerated AI methods consistently yield lower-quality solutions than KaMIS running on a single CPU core. Behavioral analysis further demonstrates that several AI models implicitly degenerate into degree-based greedy heuristics. To address this, we introduce a novel non-backtracking behavioral analysis paradigm for AI solvers, empirically exposing their strategic limitations. Notably, KaMIS is shown to significantly surpass the theoretical performance bound established by Coja-Oghlan & Efthymiou (2015) on sparse random graphs. These findings underscore that highly engineered classical solvers remain indispensable for NP-hard combinatorial optimization problems, where algorithmic sophistication and implementation efficiency outweigh current AI-driven alternatives.

Technology Category

• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Search and Optimization: Combinatorial Optimization
• Humans and AI: Other Foundations of Human Computation & AI

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

AI methods, such as generative models and reinforcement learning, have recently been applied to combinatorial optimization (CO) problems, especially NP-hard ones. This paper compares such GPU-based methods with classical CPU-based methods on Maximum Independent Set (MIS). Experiments on standard graph families show that AI-based algorithms fail to outperform and, in many cases, to match the solution quality of the state-of-art classical solver KaMIS running on a single CPU. Some GPU-based methods even perform similarly to the simplest heuristic, degree-based greedy. Even with post-processing techniques like local search, AI-based methods still perform worse than CPU-based solvers. We develop a new mode of analysis to reveal that non-backtracking AI methods, e.g. LTFT (which is based on GFlowNets), end up reasoning similarly to the simplest degree-based greedy approach, and thus worse than KaMIS. We also find that CPU-based algorithms, notably KaMIS, have strong performance on sparse random graphs, which appears to refute a well-known conjectured upper bound for efficient algorithms from Coja-Oghlan&Efthymiou (2015).

Problem

• AI methods vs classical algorithms
• Maximum Independent Set performance
• CPU-based solvers outperform AI-based methods

Innovation

• GPU-based AI methods
• comparison with CPU solvers
• non-backtracking analysis mode