Evaluating regular path queries under the all-shortest paths semantics

TL;DR

This paper presents a modified BFS algorithm to efficiently compute and enumerate all shortest paths from a source node, extending it to evaluate regular path queries with label constraints in graphs.

Contribution

It introduces a novel modification of BFS for all shortest paths and applies it to evaluate regular path queries with label restrictions.

Findings

Efficient enumeration of all shortest paths from a source node.

Extension of BFS to handle label-constrained paths in graphs.

Application to evaluate regular path queries under all-shortest paths semantics.

Abstract

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.