Implement regular path query algorithm with pathes#13
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This commit adds an implementation of the regular path query algorithm based on linear-algebra graph processing approach. The algorithm finds a set of nodes in a edge-labelled directed graph. These nodes are reachable by paths starting from one of source nodes and having edges labels conform a word from the specified regular language. This algorithm is based on the bread-first-search algorithm over the adjacency matrices. Regular languages are defined by non-deterministic finite automaton. The algorithm considers the paths on which "label words" are accepted by the specified NFA. The algorithm is used with the following inputs: * A regular automaton adjacency matrix decomposition. * A graph adjacency matrix decomposition. * An array of the starting node indices. It results with a vector, having v[i] = 1 iff the node is reachable by a path satisfying the provided regular constraints.
This patch is used to make the regular path query algorithm work with 2-RPQs. 2-RPQs represent RPQs extended with possibility of traversing graphs into the directions opposite to the presented edges. E.g. SPARQL 2-RPQ `Alice ^<mother> <daughter> ?x` could be used to find Alice and all of her sisters by getting all Alice mother's daughters. 2-RPQ support is provided by adding two extra parameters to the RPQ algorithm. One of them is used to specify some of the provided labels as inversed. The second one inverses the whole query allowing to execute single-destination RPQs (e.g. `?x <Son> Bob` gets Bob's parents).
This patch provides a workaround for benchmarking 2-RPQ algorithm on a few real-world datasets like Wikidata or yago-2s by allowing duplicates in MatrixMarket files corresponding to boolean matrices since most of the publicly available graphs likely to have duplicates.
Full description TBD.
Handle too many paths via custom arena-based linear allocator that is cleared at the end of the 2RPQ ALL PATHS procedure. It is used to construct elements of matrices having too many paths in them. It also offers OOM detection.
This patch introduces ALL SHORTEST PATH semantics in the regular path query algorithm. The key insight is really similar to the reachability (i.e. ENPOINTS) semantics described in detail in [^1]. The idea of SINGLE SOURCE ALL SHORTEST PATH semantics is for a given query $Q$, a graph $G$, and a vertex $s$ is for all vertices $v$ to find all minimum length paths from $s$ to $v$. The implementation combines custom semirings for ALL PATHS along with filtering already-visited pairs of NFA states and graph vertices. [^1] https://arxiv.org/abs/2412.10287
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