Distance oracles in edge-labeled graphs

A fundamental operation over edge-labeled graphs is the computation of shortest-path distances subject to a constraint on the set of permissible edge labels. Applying exact algorithms for such an operation is not a viable option, especially for massive graphs, or in scenarios where the distance computation is used as a primitive for more complex computations. In this paper we study the problem of efficient approximation of shortest-path queries with edge-label constraints, for which we devise two indexes based on the idea of landmarks: distances from all vertices of the graph to a selected subset of landmark vertices are pre-computed and then used at query time to efficiently approximate distance queries. The major challenge to face is that, in principle, an exponential number of constraint label sets needs to be stored for each vertex-landmark pair, which makes the index pre-computation and storage far from trivial. We tackle this challenge from two different perspectives, which lead to indexes with different characteristics: one index is faster and more accurate, but it requires more space than the other. We extensively evaluate our techniques on real and synthetic datasets, showing that our indexes can efficiently and accurately estimate label-constrained distance queries.