Evaluating regular path queries under the all-shortest paths semantics

The purpose of this report is to explain how the textbook breadth-first search algorithm (BFS) can be modified in order to also create a compact representation of all shortest paths connecting a single source node to all the nodes reachable from it. From this representation, all these paths can also be efficiently enumerated. We then apply this algorithm to solve a similar problem in edge labelled graphs, where paths also have an additional restriction that their edge labels form a word belonging to a regular language. Namely, we solve the problem of evaluating regular path queries (RPQs) under the all-shortest paths semantics.