Optimizing Key Distribution in Wireless Sensor Networks via Hybrid Graph-Theoretic and Heuristic

Wireless Sensor Networks (WSNs) face significant challenges in securing communications due to constrained node memory and computational resources. Traditional key distribution techniques often lack scalability and deterministic security guarantees. This paper proposes a novel hybrid approach combining spanning tree optimization and heuristic key assignment to maximize the number of unique cryptographic keys while ensuring network-wide connectivity. Our method transforms the key distribution problem into a degree-bounded spanning tree problem, enabling polynomial-time solutions with measurable security bounds. Experimental results on Erdos-Renyi, Barabasi-Albert, and real-world networks demonstrate that our approach reduces key path lengths by 30% compared to existing probabilistic schemes while maintaining computational efficiency. The proposed framework is adaptable to dynamic topologies, making it suitable for IoT, UAV swarms, and precision agriculture applications.