Theoretical Analysis of an Adaptive Closeness Centrality-Based Algorithm for Dynamic Optimization of Transportation Networks

Purpose: This paper presents a theoretical analysis of the DynaTrans algorithm, a novel approach for dynamic optimization of urban transportation networks. Design/methodology/approach: We introduce an Adaptive Closeness Centrality (ACC) metric and the DynaTrans algorithm, providing formal proofs of correctness, convergence, and efficiency. The analysis employs graph theory, algorithmic complexity theory, and competitive analysis techniques. Findings: We prove that DynaTrans converges to a local optimal state in O(|V|/ε) iterations, with each iteration has limited computational and memory requirements. The algorithm achieves solutions within a factor of O(log|V|) from the global optimum, outperforming simple greedy approaches. Practical implications: DynaTrans offers a theoretically sound foundation for real-time traffic management systems, potentially improving urban mobility and reducing congestion. Originality/value: This work introduces a new paradigm for dynamic transportation network optimization, combining adaptive centrality measures with efficient graph algorithms. The rigorous theoretical analysis provides a solid basis for practical implementation and future research in urban traffic management.