Choreographing the Rhythms of Observation: Dynamics for Ranged Observer Bipartite-Unipartite SpatioTemporal (ROBUST) Networks

Existing network analysis methods struggle to optimize observer placements in dynamic environments with limited visibility. This dissertation introduces the novel ROBUST (Ranged Observer Bipartite-Unipartite SpatioTemporal) framework, offering a significant advancement in modeling, analyzing, and optimizing observer networks within complex spatiotemporal domains. ROBUST leverages a unique bipartite-unipartite approach, distinguishing between observer and observable entities while incorporating spatial constraints and temporal dynamics. This research extends spatiotemporal network theory by introducing novel graph-based measures, including myopic degree, spatial closeness centrality, and edge length proportion. These measures, coupled with advanced clustering techniques like Proximal Recurrence, provide insights into network structure, resilience, and the effectiveness of observer placements. The ROBUST framework demonstrates superior resource allocation and strategic responsiveness compared to conventional models. Case studies in oceanographic monitoring, urban safety networks, and multi-agent path planning showcases its practical applicability and adaptability. Results demonstrate significant improvements in coverage, response times, and overall network efficiency. This work paves the way for future research in incorporating imperfect knowledge, refining temporal pathing methodologies, and expanding the scope of applications. By bridging theoretical advancements with practical solutions, ROBUST stands as a significant contribution to the field, promising to inform and inspire ongoing and future endeavors in network optimization and multi-agent system planning.