Path Queries Research Articles

A Knowledge Graph Embedding Model Based on Cyclic Consistency—Cyclic_CKGE

Most of the existing medical knowledge maps are incomplete and need to be completed/predicted to obtain a complete knowledge map. To solve this problem, we propose a knowledge graph embedding model (Cyclic_CKGE) based on cyclic consistency. The model first uses the “graph” constructed with the head entity and relationship to predict the tail entity, and then uses the “inverse graph” constructed with the tail entity and relationship to predict the head entity. Finally, the semantic space distance between the head entity and the original head entity should be very close, which solves the reversibility problem of the network. The Cyclic_CKGE model with a parameter of 0.46 M has the best results on FB15k-237, reaching 0.425 Hits@10. Compared with the best model R-GCN, its parameter exceeds 8 M and reaches 0.417 Hits@10. Overall, Cyclic_CKGE’s parametric efficiency is more than 17 times that of R-GCNs and more than 8 times that of DistMult. In order to better show the practical application of the model, we construct a visual medical information platform based on a medical knowledge map. The platform has three kinds of disease information retrieval methods: conditional query, path query and multi-symptom disease inference. This provides a theoretical method and a practical example for realizing knowledge graph visualization.

Fully Dynamic Contraction Hierarchies with Label Restrictions on Road Networks

In the real world, road networks with weight and label on edges can be applied in several application domains. The shortest path query with label restrictions has been receiving increasing attention recently. To efficiently answer such kind of queries, a novel index, namely Contraction Hierarchies with Label Restrictions (CHLR), is proposed in the literature. However, existing studies mainly focus on the static road networks and do not support the CHLR maintenance when the road networks are dynamically changed. Motivated by this, in this paper, we investigate the CHLR maintenance problem in dynamic road networks. We first devise a baseline approach to update CHLR by recomputing the potential affected shortcuts. However, many shortcuts recomputed in baseline do not change in fact, which leads to unnecessary overhead of the baseline. To overcome the drawbacks of baseline, we further propose a novel CHLR maintenance algorithm which can only travel little shortcuts through an update propagate chain with accuracy guarantee. Moreover, an optimization strategy is presented to further improve the efficiency of index maintenance. Considering the frequency of edge changes, we also propose a batch index maintenance algorithm to handle batch edge changes which can process a large number of edge changes at once. Furthermore, a parallel method is proposed to further accelerate calculations. Extensive and comprehensive experiments are conducted on real road networks. The experimental results demonstrate the efficiency and effectiveness of our proposed algorithms.

Query Path Generation via Bidirectional Reasoning for Multihop Question Answering From Knowledge Bases

Multi-hop question answering from knowledge bases (KBQA) is a hot research topic in natural language processing. Recently, graph neural network-based (GNN-based) methods have achieved promising results as the KB can be organized as a knowledge graph (KG). However, they often suffered from the sparsity of the KG which was detrimental to the structure-encoding and reasoning capabilities of GNN. Specifically, a KG is a sparse graph linked by directed relations and previous studies have paid scant attention to the directional characteristic of relations in the KG, limiting the patterns of relation path that GNN-based approaches could resolve. This study proposes a bidirectional recurrent graph neural network (BRGNN) to tackle these difficulties. To model the bidirectional information of relations, all adjacent relations of an entity are grouped by their directions, and they are separately aggregated into the entity representation in outward and inward directions. For the reasoning process, BRGNN simultaneously considers the neighbor relations in both directions to cover more patterns of relation paths and improve the recall of answers. Extensive experiments on three benchmarks: WebQuestionsSP, ComplexWebQuestions and MetaQA, verify that BRGNN can answer more questions by taking into account the directional information, and it is competitive to all state-of-the-art approaches.

MillenniumDB: An Open-Source Graph Database System

ABSTRACT In this systems paper, we present MillenniumDB: a novel graph database engine that is modular, persistent, and open source. MillenniumDB is based on a graph data model, which we call domain graphs, that provides a simple abstraction upon which a variety of popular graph models can be supported, thus providing a flexible data management engine for diverse types of knowledge graph. The engine itself is founded on a combination of tried and tested techniques from relational data management, state-of-the-art algorithms for worst-case-optimal joins, as well as graph-specific algorithms for evaluating path queries. In this paper, we present the main design principles underlying MillenniumDB, describing the abstract graph model and query semantics supported, the concrete data model and query syntax implemented, as well as the storage, indexing, query planning and query evaluation techniques used. We evaluate MillenniumDB over real-world data and queries from the Wikidata knowledge graph, where we find that it outperforms other popular persistent graph database engines (including both enterprise and open source alternatives) that support similar query features.

A Multi-hop Path Query Answering Model for Knowledge Graph based on Neighborhood Aggregation and Transformer

Multi-hop path query answering is a complex task in which a path needs to be inferred from a knowledge graph that contains a head entity and multi-hop relations. The objective is to identify the corresponding tail entity accurately. The representation of the path is a critical factor in this task. However, existing methods do not adequately consider the context information of the entities and relations in the path. To address this issue, this paper proposes a novel multi-hop path query answering model that utilizes an enhanced reasoning path feature representation to incorporate intermediate entity information and improve the accuracy of path query answering. The proposed model utilizes the neighborhood to aggregate the entity representation in the reasoning path. It employs a recurrent skipping network to splice the embedding of the relationship and the entity in the reasoning path based on their weight. Additionally, the model adds the position representation to obtain the reasoning path representation. Moreover, the model uses Bi-GRU and Transformer to obtain the local and global context features of each entity in the reasoning path. Finally, the reasoning path feature representation is input into the feedforward neural network and predicted through the softmax layer. The effectiveness of the proposed model in addressing the multi-hop path query answering task is demonstrated by experimental results on the WN18RR and FB15K-237 datasets. Specifically, the proposed model outperforms existing methods in terms of accuracy.

An efficient approach for faster matching of approximate patterns in graphs

Graphs have proven to be an efficient problem representation scheme in many real-world applications and can serve to address mining of patterns in large volumes of data. This work addresses the data management issue in graph databases for shortest path queries, verification of reachability, and pattern matching queries. The key issue is to match all possible patterns in a large data graph that matches a user-provided pattern, known as the query graph. The large size of the graph makes the problem complex when searching for all patterns that are similar to the user’s query. For a given query, a match occurs when a graph with n vertices has the same label as the corresponding vertices in the query graph. This work addresses such pattern matching query problems on large graphs and presents an efficient algorithm to mine all patterns that satisfies the given query. The current work presents a novel Fast Graph Pattern (FGP) mining algorithm that performs a label-specific walk on a graph and stores all vertices that are visited during the walk and hashes them on a labeled root. Experiments are performed using five benchmark datasets, and the proposed approach is compared with three state-of-the-art methods. The obtained results suggest better performance of the current proposal by achieving five times quicker results.

QHL: A Fast Algorithm for Exact Constrained Shortest Path Search on Road Networks

Route planning is fundamental in our daily life. However, existing mapping applications focus on recommending routes by optimizing one single objective, which is inconsistent with some scenarios where users prefer the optimal route under a constraint. The constrained shortest path (CSP) query matches this requirement, but the query efficiencies of previous solutions are often low due to CSP's NP-hardness. In the era of big data, state-of-the-art indexes are getting larger to support faster query processing. Recent attempts to preprocess more intermediate results and reduce the number of table lookups have proved successful in solving the CSP. However, the best-known algorithm ignores some information in the CSP queries and tries to solve a more general problem before tackling the exact CSP. In this paper, we propose by far the fastest algorithm called QHL, which fully utilizes the pruning power of the CSP query information. Specifically, we preprocess our index by generating pruning conditions that can improve query efficiency. We also conducted extensive experiments on real-world datasets to demonstrate the superiority of our proposed algorithm. QHL could answer each CSP query in around 50 μs and run faster than the best-known algorithm by orders of magnitude.

MillenniumDB: An Open-Source Graph Database System

Abstract In this systems paper, we present MillenniumDB: a novel graph database engine that is modular, persistent, and open source. MillenniumDB is based on a graph data model, which we call domain graphs, that provides a simple abstraction upon which a variety of popular graph models can be supported, thus providing a flexible data management engine for diverse types of knowledge graph. The engine itself is founded on a combination of tried and tested techniques from relational data management, state-of-the-art algorithms for worst-case-optimal joins, as well as graph-specific algorithms for evaluating path queries. In this paper, we present the main design principles underlying MillenniumDB, describing the abstract graph model and query semantics supported, the concrete data model and query syntax implemented, as well as the storage, indexing, query planning and query evaluation techniques used. We evaluate MillenniumDB over real-world data and queries from the Wikidata knowledge graph, where we find that it outperforms other popular persistent graph database engines (including both enterprise and open source alternatives) that support similar query features.

Representative dissimilar path queries: accommodating human movement dynamics in road networks

We introduce a representative dissimilar path (RDP) query, a novel type of path query in road networks. The k representative paths (RPs) between a source and a destination locations have k smallest costs for a feature (e.g., length, number of road intersections, or straightness). Given x features and k, an RDP query returns a set of paths for a source-destination pair such that the path set includes at least one of the k RPs for every feature, and the path set's similarity score is minimized. We formulate a novel measure to quantify the similarity of a set of paths. Considering different road features and incorporating the novel similarity measure in the computation of RDPs allow us to accommodate the human movement dynamics between two locations in an effective way. Finding the RDPs is a computational challenge because an RDP query requires computing the RPs for multiple features and then finding the RDPs from an exponential number of path combinations. We develop an efficient solution to answer RDP queries. The underlying ideas behind the efficiency of our algorithms are the refinement of the search space, finding the RPs for multiple features with a single search, and exploiting both the lower and upper bounds of the path set's similarity score while identifying the RDPs. We show the efficacy of the RDP query and the efficiency of our solution to answer the RDP query in extensive experiments using real datasets.

Multiple context-free path querying by matrix multiplication

Many graph analysis problems can be formulated as formal language-constrained path querying problems where the formal languages are used as constraints for navigational path queries. Recently, the context-free language (CFL) reachability formulation has become very popular and can be used in many areas, for example, querying graph databases, Resource Description Framework (RDF) analysis. However, the generative capacity of context-free grammars (CFGs) is too weak to generate some complex queries, for example, from natural languages, and the various extensions of CFGs have been proposed. Multiple context-free grammar (MCFG) is one of such extensions of CFGs. Despite the fact that, to the best of our knowledge, there is no algorithm for MCFL-reachability, this problem is known to be decidable. This paper is devoted to developing the first such algorithm for the MCFL-reachability problem. The essence of the proposed algorithm is to use a set of Boolean matrices and operations on them to find paths in a graph that satisfy the given constraints. The main operation here is Boolean matrix multiplication. As a result, the algorithm returns a set of matrices containing all information needed to solve the MCFL-reachability problem. The presented algorithm is implemented in Python using GraphBLAS API. An analysis of real RDF data and synthetic graphs for some MCFLs is performed. The study showed that using a sparse format for matrix storage and parallel computing for graphs with tens of thousands of edges the analysis time can be 10–20 minutes. The result of the analysis provides tens of millions of reachable vertex pairs. The proposed algorithm can be applied in problems of static code analysis, bioinformatics, network analysis, as well as in graph databases when a path query cannot be expressed using context-free grammars. The provided algorithm is linear algebra-based, hence, it allows one to use high-performance libraries and utilize modern parallel hardware.

Cybersecurity knowledge graph enabled attack chain detection for cyber-physical systems

The Cyber-Physical System covers a wide range of applications, many of which are involved in critical infrastructure, and the cybersecurity attacks on them become more and more threatening. Currently, most of the comprehensive analysis of compound attacks depend on the experience of security analysts. To improve the efficiency and accuracy of compound attack research, this paper introduces a knowledge graph into compound attack detection and constructs a cybersecurity knowledge graph based on the knowledge of known attacks. The cybersecurity knowledge graph can carry out correlation analysis on real-time data to restore the attack process. The main work of this paper is to construct the cybersecurity knowledge graph and to apply mining found compound attacks automatically. Besides, a multi-dimensional data association analysis algorithm based on dynamic clustering mechanism, and an attack chain complementation-pruning method based on optimal reaching path queries are proposed to solve the problem of low efficiency in correlation analysis caused by redundant data and the problem of missing and misunderstandings in the collection data. Experiments show that the cyber security knowledge graph construction method and attack chain optimization-pruning method proposed in this paper improve the accuracy and efficiency of attack chain mining.

When hierarchy meets 2-hop-labeling: efficient shortest distance and path queries on road networks

When hierarchy meets 2-hop-labeling: efficient shortest distance and path queries on road networks

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.

Analysing River Systems with Time Series Data Using Path Queries in Graph Databases

Transportation networks are used in many application areas, like traffic control or river monitoring. For this purpose, sensors are placed in strategic points in the network and they send their data to a central location for storage, viewing and analysis. Recent work proposed graph databases to represent transportation networks, since these networks can change over time, a temporal graph data model is required to keep track of these changes. In this model, time-series data are represented as properties of nodes in the network, and nodes and edges are timestamped with their validity intervals. In this paper, we show that transportation networks can be represented and queried using temporal graph databases and temporal graph query languages. Many interesting situations can be captured by the temporal paths supported by this model. To achieve the above, we extend a recently introduced temporal graph data model and its high-level query language T-GQL to support time series in the nodes of the graph, redefine temporal paths and study and implement new kinds of paths, namely Flow paths and Backwards Flow paths. Further, we analyze a real-world case, using a portion of the Yser river in the Flanders’ river system in Belgium, where some nodes are equipped with sensors while other ones are not. We model this river as a temporal graph, implement it using real data provided by the sensors, and discover interesting temporal paths based on the electric conductivity parameter, that can be used in a decision support environment, by experts for analyzing water quality across time.

Using Incremental Many-to-One Queries to Build a Fast and Tight Heuristic for A* in Road Networks

We study exact, efficient, and practical algorithms for route planning applications in large road networks. On the one hand, such algorithms should be able to answer shortest path queries within milliseconds. On the other hand, routing applications often require integrating the current traffic situation, planning ahead with predictions for future traffic, respecting forbidden turns, and many other features depending on the specific application. Therefore, such algorithms must be flexible and able to support a variety of problem variants. In this work, we revisit the A* algorithm to build a simple, extensible, and unified algorithmic framework applicable to many route planning problems. A* has been previously used for routing in road networks. However, its performance was not competitive because no sufficiently fast and tight distance estimation function was available. We present a novel, efficient, and accurate A* heuristic using Contraction Hierarchies, another popular speedup technique. The core of our heuristic is a new Contraction Hierarchies query algorithm called Lazy RPHAST , which can efficiently compute shortest distances from many incrementally provided sources toward a common target. Additionally, we describe A* optimizations to accelerate the processing of low-degree vertices, which are typical in road networks, and present a new pruning criterion for symmetrical bidirectional A*. An extensive experimental study confirms the practicality of our approach for many applications.

Directed Shortest Paths via Approximate Cost Balancing

We present an O(nm) algorithm for all-pairs shortest paths computations in a directed graph with n nodes, m arcs, and nonnegative integer arc costs. This matches the complexity bound attained by Thorup [ 31 ] for the all-pairs problems in undirected graphs. The main insight is that shortest paths problems with approximately balanced directed cost functions can be solved similarly to the undirected case. The algorithm finds an approximately balanced reduced cost function in an O(m √ n log n ) preprocessing step. Using these reduced costs, every shortest path query can be solved in O(m) time using an adaptation of Thorup’s component hierarchy method. The balancing result can also be applied to the ℓ ∞ -matrix balancing problem.

Proximity Queries on Terrain Surface

Due to the advance of the geo-spatial positioning and the computer graphics technology, digital terrain data has become increasingly popular nowadays. Query processing on terrain data has attracted considerable attention from both the academic and the industry communities. Proximity queries such as the shortest path/distance query, k nearest/farthest neighbor query, and top- k closest/farthest pairs query are fundamental and important queries in the context of the terrain surfaces, and they have a lot of applications in Geographical Information System, 3D object feature vector construction, and 3D object data mining. In this article, we first study the most fundamental type of query, namely, shortest distance and path query, which is to find the shortest distance and path between two points of interest on the surface of the terrain. As observed by existing studies, computing the exact shortest distance/path is very expensive. Some existing studies proposed ϵ -approximate distance and path oracles, where ϵ is a non-negative real-valued error parameter. However, the best-known algorithm has a large oracle construction time, a large oracle size, and a large query time. Motivated by this, we propose a novel ϵ -approximate distance and path oracle called the S pace E fficient distance and path oracle (SE), which has a small oracle construction time, a small oracle size, and a small distance and path query time, thanks to its compactness of storing concise information about pairwise distances between any two points-of-interest. Then, we propose several algorithms for the k nearest/farthest neighbor and top- k closest/farthest pairs queries with the assistance of our distance and path oracle SE . Our experimental results show that the oracle construction time, the oracle size, and the distance and path query time of SE are up to two, three, and five orders of magnitude faster than the best-known algorithm, respectively. Besides, our algorithms for other proximity queries including k nearest/farthest neighbor queries and top- k closest/farthest pairs queries significantly outperform the state-of-the-art algorithms by up to two orders of magnitude.

Shortest Beer Path Queries in Outerplanar Graphs

A beer graph is an undirected graph G, in which each edge has a positive weight and some vertices have a beer store. A beer path between two vertices u and v in G is any path in G between u and v that visits at least one beer store. We show that any outerplanar beer graph G with n vertices can be preprocessed in O(n) time into a data structure of size O(n), such that for any two query vertices u and v, (i) the weight of the shortest beer path between u and v can be reported in \(O(\alpha (n))\) time (where \(\alpha (n)\) is the inverse Ackermann function), and (ii) the shortest beer path between u and v can be reported in O(L) time, where L is the number of vertices on this path. Note that the running time for (ii) does not depend on the number of vertices of G. Both results are optimal, even when G is a beer tree (i.e., a beer graph whose underlying graph is a tree).

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.

A workload-driven method for designing aggregate-oriented NoSQL databases

Due to the scalability and availability problems with traditional relational database systems, a variety of NoSQL stores have emerged over the last decade to deal with big data. How data are structured in a NoSQL store has a large impact on the query and update performance and the storage usage. Thus, different from the traditional database design, not only the data structure but also the data access patterns need to be considered in the design of NoSQL database schemas. In this paper, we present a general workload-driven method for designing key-value, wide-column, and document NoSQL database schemas. We first present a generic logical model Query Path Graph (QPG) that can represent the data structures of the UML class diagram. We also define mappings from the SQL-based query patterns to QPG and from QPG to aggregate-oriented NoSQL schemas. We use a cost model to measure the query and update performance and optimize the QPG schemas. We evaluate the proposed method with several typical case studies by simulating workloads on databases with different schema designs. The results demonstrate that our method preserves the generality and the quality of the design.