A note on exact distance labeling

We show that the vertices of an edge-weighted undirected graph can be labeled with labels of size O(n) such that the exact distance between any two vertices can be inferred from their labels alone in O(log^@?n) time. This improves the previous best exact distance labeling scheme that also requires O(n)-sized labels but O(loglogn) time to compute the distance. Our scheme is almost optimal as exact distance labeling is known to require labels of length @W(n).