The c-packedness property, proposed in 2010, is a geometric property that captures the spatial distribution of a set of edges. Despite the recent interest in c-packedness, its utility has so far been limited to Fréchet distance problems. An open problem is whether a wider variety of algorithmic and data structure problems can be solved efficiently under the c-packedness assumption, and more specifically, on c-packed graphs. In this paper, we prove two fundamental properties of c-packed graphs: that there exists a linear-size well-separated pair decomposition under the graph metric, and there exists a constant size balanced separator. We then apply these fundamental properties to obtain a small tree cover for the metric space and distance oracles under the shortest path metric. In particular, we obtain a tree cover of constant size, an exact distance oracle of near-linear size and an approximate distance oracle of linear size.
Deryckere et al. (Wed,) studied this question.