Wave-Based Computing for Solving NP-Hard Problems: A Mathematical Framework and Applications

This paper explores the use of wave-based computing as a novel computational framework for solving NP-hard problems such as the Traveling Salesman Problem (TSP) and the Set Cover Problem (SCP). Wave-based computing leverages interference phenomena, amplitude modulation, and energy minimization principles to efficiently explore solution spaces. We present a mathematical model that maps NP-hard problems onto wave dynamics, enabling the discovery of near-optimal solutions with reduced computational complexity. Experimental results demonstrate the algorithm's effectiveness in minimizing costs and achieving high-quality solutions compared to traditional methods. This work lays the foundation for applying wave-based computing to optimization challenges in logistics, network design, and quantum-inspired systems.