Bridging Pattern-Aware Complexity with NP-Hard Optimization: A Unifying Framework and Empirical Study
This provides a practical, unified approach for improving efficiency in domains like financial forecasting and LLM optimization, though it is incremental relative to theoretical NP-hardness.
The paper tackles NP-hard optimization problems by proposing a pattern-aware complexity framework that leverages structural regularities to reduce computational complexity, achieving up to 79% solution quality gains in Traveling Salesman Problem benchmarks.
NP hard optimization problems like the Traveling Salesman Problem (TSP) defy efficient solutions in the worst case, yet real-world instances often exhibit exploitable patterns. We propose a novel patternaware complexity framework that quantifies and leverages structural regularities e.g., clustering, symmetry to reduce effective computational complexity across domains, including financial forecasting and LLM optimization. With rigorous definitions, theorems, and a meta learning driven solver pipeline, we introduce metrics like Pattern Utilization Efficiency (PUE) and achieve up to 79 percent solution quality gains in TSP benchmarks (22 to 2392 cities). Distinct from theoretical NP hardness, our approach offers a unified, practical lens for pattern-driven efficiency.