Bridging Pattern-Aware Complexity with NP-Hard Optimization: A Unifying Framework and Empirical Study

TL;DR

This paper introduces a pattern-aware complexity framework that leverages structural regularities in NP-hard problems to improve solution efficiency, demonstrated through a meta-learning solver achieving significant quality gains in TSP benchmarks.

Contribution

It presents a unifying, practical framework for exploiting patterns in NP-hard problems, including new metrics and a solver pipeline that enhances solution quality.

Findings

Achieved up to 79% solution quality improvements in TSP benchmarks.

Developed metrics like Pattern Utilization Efficiency (PUE).

Provided a theoretical foundation with definitions and theorems.

Abstract

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.