Explaining results of path queries on graphs: Single-path results for context-free path queries

Many graph query languages use, at their core, path queries that yield node pairs $(m,n)$ that are connected by a path of interest. For the end-user, such node pairs only give limited insight as to why this result is obtained, as the pair does not directly identify the underlying path of interest.

In this paper, we propose the single-path semantics to address this limitation of path queries. Under single-path semantics, path queries evaluate to a single path connecting nodes $m$ and $n$ and that satisfies the conditions of the query. To put our proposal in practice, we provide an efficient algorithm for evaluating context-free path queries using the single-path semantics. Additionally, we perform a short evaluation of our techniques that shows that the single-path semantics is practically feasible, even when query results grow large.

In addition, we explore the formal relationship between the single-path semantics we propose the problem of finding the shortest string in the intersection of a regular language (representing a graph) and a context-free language (representing a path query). As our formal results show, there is a distinction between the complexity of the single-path semantics for queries that use a single edge label and queries that use multiple edge labels: for queries that use a single edge label, the length of the shortest path is linearly upper bounded by the number of nodes in the graph; whereas for queries that use multiple edge labels, the length of the shortest path has a worst-case quadratic lower bound.