Dominance-Based Boundary Nodes Finding Algorithm (DBBNFA) and its application to WSN

This paper introduces a novel and efficient algorithm named Dominance-Based Boundary Nodes Finding Algorithm (DBBNFA). The DBBNFA applies the Pareto dominance principle to identify boundary nodes within a set of points or nodes in an N-dimensional space, such as a cloud or graph. Its core concept combines four Pareto frontiers, each detecting one-quarter of the boundary, resulting in a complete and accurate delineation. This approach ensures robust performance and scalability, making it well-suited for distributed systems. Several versions of the DBBNFA address diverse data structures and use cases. The global dominance-based version (G-DBBNFA) is optimized for datasets with a single convex cluster and no internal openings. A more flexible variant, the local dominance-based (L-DBBNFA), handles convex, concave,multi-cluster datasets, and those with holes. Distributed versions (D-DBBNFA) are ideal for decentralized environments, including the basic D-DBBNFA for direct neighbors, the Deep-D-DBBNFA for indirect neighbors, and the Deep-D-DBBNFA with an embedded D-LPCN for advanced processing. Extensive evaluations confirm the algorithm's high precision and scalability. Both G-DBBNFA and L-DBBNFA were rigorously tested on diverse datasets, while D-DBBNFA was evaluated on wireless sensor networks with complex topologies using the CupCarbon simulator. The results highlight DBBNFA as a powerful tool for boundary node detection in centralized and distributed systems.