  Measuring the distances between vertices on graphs is one of the most
fundamental components in network analysis. Since finding shortest paths
requires traversing the graph, it is challenging to obtain distance information
on large graphs very quickly. In this work, we present a preprocessing
algorithm that is able to create landmark based distance sketches efficiently,
with strong theoretical guarantees. When evaluated on a diverse set of social
and information networks, our algorithm significantly improves over existing
approaches by reducing the number of landmarks stored, preprocessing time, or
stretch of the estimated distances.
  On Erd\"{o}s-R\'{e}nyi graphs and random power law graphs with degree
distribution exponent $2 < \beta < 3$, our algorithm outputs an exact distance
data structure with space between $\Theta(n^{5/4})$ and $\Theta(n^{3/2})$
depending on the value of $\beta$, where $n$ is the number of vertices. We
complement the algorithm with tight lower bounds for Erdos-Renyi graphs and the
case when $\beta$ is close to two.
