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The goal of a hub-based distance labeling scheme for a network G = (V, E) isto assign a small subset S(u) $\subseteq$ V to each node u $\in$ V, in such away that for any pair of nodes u, v, the intersection of hub sets S(u) $\cap$S(v) contains a node on the shortest uv-path. The existence of small hub sets,and consequently efficient shortest path processing algorithms, for roadnetworks is an empirical observation. A theoretical explanation for thisphenomenon was proposed by Abraham et al. (SODA 2010) through a networkparameter they called highway dimension, which captures the size of a hittingset for a collection of shortest paths of length at least r intersecting agiven ball of radius 2r. In this work, we revisit this explanation, introducinga more tractable (and directly comparable) parameter based solely on thestructure of shortest-path spanning trees, which we call skeleton dimension. Weshow that skeleton dimension admits an intuitive definition for both directedand undirected graphs, provides a way of computing labels more efficiently thanby using highway dimension, and leads to comparable or stronger theoreticalbounds on hub set size.

Beyond Highway Dimension: Small Distance Labels Using Tree Skeletons