A note on exact distance labeling

Abstract

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 ( log log n ) time to compute the distance. Our scheme is almost optimal as exact distance labeling is known to require labels of length Ω ( n ) .