Fast Temporal Path Localization on Graphs via Multiscale Viterbi Decoding

We consider a problem of localizing a temporal path signal that evolves over time on a graph. A path signal represents the trajectory of a moving agent on a graph in a series of consecutive time stamps. Through combining dynamic programing and graph partitioning, we propose a path-localization algorithm with significantly reduced computational complexity. To analyze the localization performance, we use two evaluation metrics to quantify the localization error: the Hamming distance and the destination's distance between the ground-truth path and the estimated path. In random geometric graphs, we provide a closed-form expression for the localization error bound, and a tradeoff between localization error and the computational complexity. Finally, we compare the proposed technique with the maximum likelihood estimate in terms of computational complexity and localization error, and show significant speedup (100×) with comparable localization error (4×) on a graph from real data.