Regular Path Queries Research Articles

Materialized View Selection & View-Based Query Planning for Regular Path Queries

A regular path query (RPQ) returns node pairs connected by a path whose edge label sequence satisfies the given regular expression. Given a workload of RPQs, selecting the shared subqueries as materialized views to precompute offline can speed up the online processing. Since the available memory is limited, we define the materialized view selection (MVS) problem for RPQs as minimizing the total workload query cost within a memory budget. To tackle the problem's NP-hardness, we design an efficient MVS algorithm based on heuristics. To prevent redundancies in the selected views, we devise the AND-OR directed acyclic graph with closure (AODC) as the multi-RPQ query plan representation for the workload, which encodes the relations between subqueries. In addition to detecting view redundancy, the AODC also incrementally updates itself during view selection. To support query planning, we design a scalable cost and cardinality estimation scheme for full-fledged RPQs, including Kleene closures. Our method, when applied to the Wikidata Query Logs, shows a 9.73× speedup in the total query processing time compared to ad-hoc processing, using the views it selects.

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.

MWP: Multi-Window Parallel Evaluation of Regular Path Queries on Streaming Graphs

A persistent Regular Path Query (RPQ) on a streaming graph is to continuously find every pair of vertices that are connected by a path in the graph within a sliding window, such that the edge label sequence of this path matches a given regular expression. The existing RPQ evaluation algorithm in the literature incrementally maintains a set of spanning-tree-like data structures to quickly form query results and to avoid reprocessing edges that are shared by multiple sliding windows. This approach allows parallel processing of the graph edges within a sliding window but requires a blocking expiration phase between sliding windows to remove the old edges. This blocking phase can significantly degrade the query performance, especially when the edges arrive quickly and the sliding windows overlap significantly. This paper presents a new RPQ evaluation strategy called Multi-Window Parallel (MWP) method leveraging a new data structure called Timestamped Rooted Digraph (TRD). The novel idea is to incrementally maintain TRDs for the quick formulation of query results, like the aforementioned spanning trees, but simultaneously contain needed information for multiple sliding windows. MWP eliminates the forced blocking expiration phase. Only when memory runs low, a quick "dirty garbage collection" (DGC) process is done to remove some unneeded edges and nodes on TRDs, without incurring large costs. Extensive experiments on real graph datasets show that MWP significantly outperforms the existing algorithm in terms of throughput, tail latency, and scalability, and that DGC provides an effective solution for releasing memory with minimum impact.

Efficient Regular Simple Path Queries under Transitive Restricted Expressions

Efficient Regular Simple Path Queries under Transitive Restricted Expressions

LM-SRPQ: Efficiently Answering Regular Path Query in Streaming Graphs

Regular path query (RPQ) is a basic operation for graph data analysis, and persistent RPQ in streaming graphs is a new-emerging research topic. In this paper, we propose a novel algorithm for persistent RPQ in streaming graphs, named LM-SRPQ. It solves persistent RPQ with a combination of intermediate result materialization and real-time graph traversal. Compared to prior art, it merges redundant storage and computation, achieving higher memory and time efficiency. We carry out extensive experiments with both real-world and synthetic streaming graphs to evaluate its performance. Experiment results confirm its superiority compared to prior art in both memory and time efficiency.

A Trichotomy for Regular Trail Queries

Regular path queries (RPQs) are an essential component of graph query languages. Such queries consider a regular expression r and a directed edge-labeled graph G and search for paths in G for which the sequence of labels is in the language of r. In order to avoid having to consider infinitely many paths, some database engines restrict such paths to be trails, that is, they only consider paths without repeated edges. In this paper we consider the evaluation problem for RPQs under trail semantics, in the case where the expression is fixed. We show that, in this setting, there exists a trichotomy. More precisely, the complexity of RPQ evaluation divides the regular languages into the finite languages, the class Ttract (for which the problem is tractable), and the rest. Interestingly, the tractable class in the trichotomy is larger than for the trichotomy for simple paths, discovered by Bagan, Bonifati, and Groz [JCSS 2020]. In addition to this trichotomy result, we also study characterizations of the tractable class, its expressivity, the recognition problem, closure properties, and show how the decision problem can be extended to the enumeration problem, which is relevant to practice.

Fine-Grained Complexity of Regular Path Queries

A regular path query (RPQ) is a regular expression q that returns all node pairs (u, v) from a graph database that are connected by an arbitrary path labelled with a word from L(q). The obvious algorithmic approach to RPQ-evaluation (called PG-approach), i.e., constructing the product graph between an NFA for q and the graph database, is appealing due to its simplicity and also leads to efficient algorithms. However, it is unclear whether the PG-approach is optimal. We address this question by thoroughly investigating which upper complexity bounds can be achieved by the PG-approach, and we complement these with conditional lower bounds (in the sense of the fine-grained complexity framework). A special focus is put on enumeration and delay bounds, as well as the data complexity perspective. A main insight is that we can achieve optimal (or near optimal) algorithms with the PG-approach, but the delay for enumeration is rather high (linear in the database). We explore three successful approaches towards enumeration with sub-linear delay: super-linear preprocessing, approximations of the solution sets, and restricted classes of RPQs.

Representing Paths in Graph Database Pattern Matching

Modern graph database query languages such as GQL, SQL/PGQ, and their academic predecessor G-Core promote paths to first-class citizens in the sense that their pattern matching facility can return paths , as opposed to only nodes and edges. This is challenging for database engines, since graphs can have a large number of paths between a given node pair, which can cause huge intermediate results in query evaluation. We introduce the concept of path multiset representations (PMRs) , which can represent multisets of paths exponentially succinctly and therefore bring significant advantages for representing intermediate results. We give a detailed theoretical analysis that shows that they are especially well-suited for representing results of regular path queries and extensions thereof involving counting, random sampling, and unions. Our experiments show that they drastically improve scalability for regular path query evaluation, with speedups of several orders of magnitude.

Answering regular path queries mediated by unrestricted [formula omitted] ontologies

A prime application of description logics is ontology-mediated query answering, with the query language often reaching far beyond instance queries. Here, we investigate this task for positive existential two-way regular path queries and ontologies formulated in the expressive description logic SQu, where SQu denotes the extension of the basic description logic ALC with transitive roles (S) and qualified number restrictions (Q) which can be unrestrictedly applied to both non-transitive and transitive roles (⋅u). Notably, the latter is usually forbidden in expressive description logics. As the main contribution, we show decidability of ontology-mediated query answering in that setting and establish tight complexity bounds, namely 2ExpTime-completeness in combined complexity and coNP-completeness in data complexity. Since the lower bounds are inherited from the fragment ALC, we concentrate on providing upper bounds. As main technical tools we establish a tree-like countermodel property and a characterization of when a query is not satisfied in a tree-like interpretation. Together, these results allow us to use an automata-based approach to query answering.

FPIRPQ: Accelerating regular path queries on knowledge graphs

With the growing popularity and application of knowledge-based artificial intelligence, the scale of knowledge graph data is dramatically increasing. As an essential type of query for RDF graphs, Regular Path Queries (RPQs) have attracted increasing research efforts, which explore RDF graphs in a navigational manner. Moreover, path indexes have proven successful for semi-structured data management. However, few techniques can be used effectively in practice for processing RPQ on large-scale knowledge graphs. In this paper, we propose a novel indexing solution named FPIRPQ (Frequent Path Index for Regular Path Queries) by leveraging Frequent Path Mining (FPM). Unlike the existing approaches to RPQs processing, FPIRPQ takes advantage of frequent paths, which are statistically derived from the data to accelerate RPQs. Furthermore, since there is no explicit benchmark targeted for RPQs over RDF graph yet, we design a micro-benchmark including 12 basic queries over synthetic and real-world datasets. The experimental results illustrate that FPIRPQ improves the query efficiency by up to orders of magnitude compared to the state-of-the-art RDF storage engine.

Jumping Evaluation of Nested Regular Path Queries

Nested regular path queries are used for querying graph databases and RDF triple stores. We propose a new algorithm for evaluating nested regular path queries on a graph from a set of start nodes in combined linear time. We show that this complexity upper bound can be reduced by making it dependent on the size of the query's top-down needed subgraph, a notion that we introduce. For many queries in practice, the top-down needed subgraph is way smaller than the whole graph. Our algorithm is based on a novel compilation schema from nested regular path queries to monadic datalog queries. Its complexity upper bound follows from known properties of top-down datalog evaluation. As an application, we show that our algorithm permits to reformulate in simple terms a variant of a very efficient automata-based algorithm proposed by Maneth and Nguyen that evaluates navigational path queries in datatrees based on indexes and jumping. Moreover, it overcomes some limitations of Maneth and Nguyen's: it is not bound to trees and applies to graphs; it is not limited to forward navigational XPath but can treat any nested regular path query and it can be implemented efficiently without any dedicated techniques, by using any efficient datalog evaluator such as LogicBlox.

Conjunctive Regular Path Queries with Capture Groups

In practice, regular expressions are usually extended by so-called capture groups or capture variables, which allow to capture a subexpression by a variable that can be referenced in the regular expression in order to describe repetitions of subwords. We investigate how this concept could be used for pattern-based graph querying; i.e., we investigate conjunctive regular path queries (CRPQs) that are extended by capture variables. If capture variables are added to CRPQs in a completely unrestricted way, then Boolean evaluation becomes PSPACE-hard in data complexity, even for single-edge graph patterns. On the other hand, if capture variables do not occur under a Kleene star, then the data complexity drops to NL-completeness. Combined complexity is in EXPSPACE but drops to PSPACE-completeness if the depth (i.e., the nesting depth of capture variables) is bounded, and it drops to NP-completeness if the size of the images of capture variables is bounded by a constant (regardless of the depth or of whether capture variables occur under a Kleene star). In the application of regular expressions as string searching tools, references to capture variables only describe exact repetitions of subwords (i.e., they implement the equality relation on strings). Following recent developments in graph database research, we also study CRPQs with capture variables that describe arbitrary regular relations. We show that if the expressions have depth 0, or if the size of the images of capture variables is bounded by a constant, then we can allow arbitrary regular relations while staying in the same complexity bounds. We also investigate the problems of checking whether a given tuple is in the solution set and computing the whole solution set. On the conceptual side, we add capture variables to CRPQs in such a way that they can be defined in an expression on one arc of the graph pattern but also referenced in expressions on other arcs. Hence, they add to CRPQs the possibility to define inter-dependencies between different paths, which is a relevant feature of pattern-based graph querying.

The power of Tarski's relation algebra on trees

Fragments of Tarski's relation algebra form the basis of many versatile graph and tree query languages including the regular path queries, XPath, and SPARQL. Surprisingly, however, a systematic study of the relative expressive power of relation algebra fragments on trees has not yet been undertaken. In this work, we perform such a systematic study. Our approach is to start from a basic fragment which only allows composition and union. We then study how the expressive power of the query language changes if we add diversity, converse, projections, coprojections, intersection, and/or difference, both for path queries and Boolean queries. For path queries on labeled trees, we found that adding intersection and difference yields more expressive power for some fragments, while adding one of the other operators always yields more expressive power. For Boolean queries on labeled trees, we obtain a similar picture for the relative expressive power, except for a few fragments where adding converse or projection yields no more expressive power. Additionally, we also studied querying unlabeled trees, for which we have found several redundancies. One challenging problem remains open, however, for both path and Boolean queries: does adding difference yield more expressive power to fragments containing at least diversity, coprojections, and intersection?

The Dichotomy of Evaluating Homomorphism-Closed Queries on Probabilistic Graphs

We study the problem of query evaluation on probabilistic graphs, namely, tuple-independent probabilistic databases over signatures of arity two. We focus on the class of queries closed under homomorphisms, or, equivalently, the infinite unions of conjunctive queries. Our main result states that the probabilistic query evaluation problem is #P-hard for all unbounded queries from this class. As bounded queries from this class are equivalent to a union of conjunctive queries, they are already classified by the dichotomy of Dalvi and Suciu (2012). Hence, our result and theirs imply a complete data complexity dichotomy, between polynomial time and #P-hardness, on evaluating homomorphism-closed queries over probabilistic graphs. This dichotomy covers in particular all fragments of infinite unions of conjunctive queries over arity-two signatures, such as negation-free (disjunctive) Datalog, regular path queries, and a large class of ontology-mediated queries. The dichotomy also applies to a restricted case of probabilistic query evaluation called generalized model counting, where fact probabilities must be 0, 0.5, or 1. We show the main result by reducing from the problem of counting the valuations of positive partitioned 2-DNF formulae, or from the source-to-target reliability problem in an undirected graph, depending on properties of minimal models for the query.

Answering regular path queries through exemplars

Regular simple path query (RPQ) is one of the fundamental operators in graph analytics. In an RPQ, the input is a graph, a source node and a regular expression. The goal is to identify all nodes that are connected to the source through a simple path whose label sequence satisfies the given regular expression. The regular expression acts as a formal specification of the search space that is of interest to the user. Although regular expressions have high expressive power, they act as barrier to non-technical users. Furthermore, to fully realize the power of regular expressions, the user must be familiar with the domain of the graph dataset. In this study, we address this bottleneck by bridging RPQs with the query-by-example paradigm. More specifically, we ask the user for an exemplar pair that characterizes the paths of interest, and the regular expression is automatically inferred from this exemplar. This novel problem introduces several new challenges. How do we infer the regex? Given that answering RPQs is NP-hard, how do we scale to large graphs? We address these challenges through a unique combination of Biermann and Feldman's algorithm with NFA-guided random walks with restarts. Extensive experiments on multiple real, million-scale datasets establish that RQuBE is at least 3 orders of magnitude faster than baseline strategies with an average accuracy in excess of 90%.

Answering Regular Path Queries Under Approximate Semantics in Lightweight Description Logics

Classical regular path queries (RPQs) can be too restrictive for some applications and answering such queries under approximate semantics to relax the query is desirable. While for answering regular path queries over graph databases under approximate semantics algorithms are available, such algorithms are scarce for the ontology-mediated setting. In this paper we extend an approach for answering RPQs over graph databases that uses weighted transducers to approximate paths from the query in two ways. The first extension is to answering approximate conjunctive 2-way regular path queries (C2RPQs) over graph databases and the second is to answering C2RPQs over ELH and DL-Lite_R ontologies. We provide results on the computational complexity of the underlying reasoning problems and devise approximate query answering algorithms.

Efficiently Estimating Joining Cost of Subqueries in Regular Path Queries

Evaluating Regular Path Queries (RPQs) have been of interest since they were used as a powerful way to explore paths and patterns in graph databases. Traditional automata-based approaches are restricted in the graph size and/or highly complex queries, which causes a high evaluation cost (e.g., memory space and response time) on large graphs. Recently, although using the approach based on the threshold rare label for large graphs has been achieving some success, they could not often guarantee the minimum searching cost. Alternatively, the Unit-Subquery Cost Matrix (USCM) has been studied and obtained the viability of the usage of subqueries. Nevertheless, this method has an issue, which is, it does not cumulate the cost among subqueries that causes the long response time on a large graph. In order to overcome this issue, this paper proposes a method for estimating joining cost of subqueries to accelerate the USCM based parallel evaluation of RPQs on a large graph, namely USCM-Join. Through real-world datasets, we experimentally show that the USCM-Join outperforms others and estimating the joining cost enhances the USCM based approach up to around 20% in terms of response time.

Distributed processing of regular path queries in RDF graphs

SPARQL 1.1 offers a type of navigational query for RDF systems, called regular path query (RPQ). A regular path query allows for retrieving node pairs with the paths between them satisfying regular expressions. Regular path queries are always difficult to be evaluated efficiently because of the possible large search space. Thus there has been no scalable and practical solution so far. In this paper, we present Leon+, an in-memory distributed framework, to address the RPQ problem in the context of the knowledge graph. To reduce search space and mitigate mounting communication costs, Leon+ takes advantage of join-ahead pruning via a novel RDF summarization technique together with a path partitioning strategy. We also develop a subtle cost model to devise query plans to achieve high efficiency for complex RPQs. As there has been no available RPQ benchmark, we create micro-benchmarks on both synthetic and real-world datasets. A thorough experimental evaluation is presented between our approach and the state-of-the-art RDF stores. The results show that our approach outperforms 5x faster than the competitors on single RPQ. For query workload, it saves up to 1/2 time and 2/3 communication overheads over the baseline method.

Efficient Compilation of Regular Path Queries

Ad hoc code generation is a state-of-the-art processing paradigm for database execution engines. It minimizes resource consumption by generating specialized code, tailored and streamlined for the single query at hand. In this work, we apply ad hoc code generation to regular path queries (RPQs), an advanced query type in declarative graph query languages. We investigate code generation from multiple angles. We propose COAT, an embedded domain specific language (EDSL) in C++ to improve accessibility of code generation by simplifying the interaction with compiler APIs. Furthermore, we analyze and compare two back ends for COAT providing the just-in-time (JIT) compilation functionality: LLVM, a compiler framework popularly used in databases for code generation, and AsmJit, a JIT assembler with very low compilation latency. We evaluate various compilation techniques for RPQs on different synthetic graph workloads.

Presburger Constraints in Trees

The fully enriched µ-calculus is an expressive propositional modal logic with least and greatest fixed-points, nominals, inverse programs and graded modalities. Several fragments of this logic are known to be decidable in EXPTIME. However, the full logic is undecidable. Nevertheless, it has been recently shown that the fully enriched µ-calculus is decidable in EXPTIME when its models are finite trees. In the present work, we study the fully-enriched µ-calculus for trees extended with Presburger constraints. These constraints generalize graded modalities by restricting the number of children nodes with respect to Presburger arithmetic expressions. We show that this extension is decidable in EXPTIME. In addition, we also identify decidable extensions of regular tree languages (XML schemas) with interleaving and counting operators. This is achieved by alinear characterization in terms of the logic. Regular path queries (XPath) with Presburger constraints on children paths are also characterized. These results imply new optimal reasoning (emptiness, containment, equivalence) bounds on counting extensions of XPathqueries and XML schemas.