Adaptive Spectral Privacy Budgeting for Emergency Traffic Coordination

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Publishing traffic data from road-network sensors must protect predictable, everyday movement patterns, but differentially private noise that is spread uniformly risks masking the rare signals, such as accidents, that the data is meant to help detect. Prior differentially private graph-signal mechanisms either protect the underlying network structure or apply denoising after privatization; we instead derive an a priori, closed-form noise allocation directly from a graph's spectral structure. The mechanism combines a graph Fourier transform, an independently-calibrated spectral basis, and a Lagrangian-derived allocation law using a tight, component-specific sensitivity bound. Using Rényi differential privacy composition instead of standard composition reduces required noise by 80% and improves reconstruction error by 96.9–97.4% at matched privacy guarantees, while yielding a statistically significant improvement in anomaly detectability over uniform allocation (paired test, p < 0.0001 and p = 0.023 across two budgets).