Distinct Shortest Walk Enumeration for RPQs

We consider the Distinct Shortest Walks problem. Given two vertices s and t of a graph database D and a regular path query, we want to enumerate all walks of minimal length from s to t that carry a label that conforms to the query. Usual theoretical solutions turn out to be inefficient when applied to graph models that are closer to real-life systems, in particular because edges may carry multiple labels. Indeed, known algorithms may repeat the same answer exponentially many times. We propose an efficient algorithm for graph databases with multiple labels. The preprocessing runs in O(DxA) and the delay between two consecutive outputs is in O(λxA), where A is a nondeterministic automaton representing the query and L is the minimal length. The algorithm can handle epsilon-transitions in A or queries given as regular expressions at no additional cost.