Context-free path querying by matrix multiplication

Abstract

Graph data models are widely used in many areas, for example, bioinformatics, graph databases. In these areas, it is often required to process queries for large graphs. Some of the most common graph queries are navigational queries. The result of query evaluation is a set of implicit relations between nodes of the graph, i.e. paths in the graph. A natural way to specify these relations is by specifying paths using formal grammars over the alphabet of edge labels. An answer to a context-free path query in this approach is usually a set of triples (A, m, n) such that there is a path from the node m to the node n, whose labeling is derived from a non-terminal A of the given context-free grammar. This type of queries is evaluated using the relational query semantics. Another example of path query semantics is the single-path query semantics which requires presenting a single path from the node m to the node n, whose labeling is derived from a non-terminal A for all triples (A, m, n) evaluated using the relational query semantics. There is a number of algorithms for query evaluation which use these semantics but all of them perform poorly on large graphs. One of the most common technique for efficient big data processing is the use of a graphics processing unit (GPU) to perform computations, but these algorithms do not allow to use this technique efficiently. In this paper, we show how the contextfree path query evaluation using these query semantics can be reduced to the calculation of the matrix transitive closure. Also, we propose an algorithm for context-free path query evaluation which uses relational query semantics and is based on matrix operations that make it possible to speed up computations by using a GPU.

One Algorithm to Evaluate Them All: Unified Linear Algebra Based Approach to Evaluate Both Regular and Context-Free Path Queries

“…Unfortunately, none of them has better than cubic time complexity in terms of the input graph size. The algorithm by Azimov and Grigorev (2018) is, best to our knowledge, the first algorithm for CFPQ which is based on linear algebra. It was shown by Terekhov et al (2020) that this algorithm can be applied to real-world graph analysis problems, while Kuijpers et al (2019) show that other state-of-the-art CFPQ algorithms are not performant enough to handle real-world graphs.…”

“…Evaluation of the libraries that implement this API, such as SuiteSparce (Davis, 2019) and CombBLAS (Buluç and Gilbert, 2011), show that reduction to linear algebra is a good way to utilize highperformance parallel and distributed computations for graph analysis. Azimov and Grigorev (2018) showed how to reduce CFPQ to matrix multiplication. Later, it was shown by Mishin et al (2019) and Terekhov et al (2020) that by using the appropriate libraries for linear algebra for Azimov's algorithm implementation one can create a practical solution for CFPQ.…”

A survey of typical attributed graph queries

“…Similar to RPQ, CFPQ is also in general NP-complete [79,229]. Existing approaches to CFPQ processing are heuristic methods based on matrix multiplication [4] or grammar parse table [138].…”

“…-Keyword search on knowledge graph (RDF): Resource Description Framework (RDF) is initially introduced for conceptual description of Web information in a triple form (sub, pred, obj). Recently, RDF has attracted much interest from both academic and industrial communities due to the prevalence of large-scale knowledge bases, such as DBPedia [3], Yago [172], Freebase [17], and Google Knowledge Graph 4 . RDF data can be naturally formalized as attributed graphs.…”

Path querying on acyclic graphs using Boolean grammars

“…Вопрос использования контекстно-свободных грамматик в качестве ограничений для поиска путей активно исследуется в настоящее время [14,16]. Предложены эффективные алгоритмы выполнения соответствующих запросов к графам [17,18,19]. Алгоритм выполнения запросов с ограничениями в терминах контекстно-свободных грамматик, основанный на синтаксическом анализе «сверху вниз» [32], представлен в работе [31].…”