Provenance for Regular Path Queries

Regular path queries (RPQs) the ubiquitous mechanism for querying data graphs of partially known structure. RPQs are in essence regular expressions over the edge symbols. The answer to an RPQ on a given graph (database) is the set of pairs of objects, which are connected by paths spelling words in the language of the regular path query. Often the database edges come with a weights assoaciated to them. Such weights can distances, levels of discomfort, multiplicities, etc. We model weights using semiring frameworks

Efficient Exact Paths For Dyck and semi-Dyck Labeled Path Reachability

The exact path length problem is to determine if there is a path of a given fixed cost between two vertices. This paper focuses on the exact path problem for costs $-1,0$ or $+1$ between all pairs of vertices in an edge-weighted digraph. The edge weights are from $\{ -1, +1 \}$. In this case, this paper gives an $\widetilde{O}(n^{\omega})$ exact path solution. Here $\omega$ is the best exponent for matrix multiplication and $\widetilde{O}$ is the asymptotic upper-bound mod polylog factors. Variations of this algorithm determine which pairs of digraph nodes have Dyck or semi-Dyck labeled paths between them, assuming two parenthesis. Therefore, determining digraph reachability for Dyck or semi-Dyck labeled paths costs $\widetilde{O}(n^{\omega})$. A path label is made by concatenating all symbols along the path's edges. The exact path length problem has many applications. These applications include the labeled path problems given here, which in turn, also have numerous applications