Path Queries Research Articles

Explaining results of path queries on graphs: Single-path results for context-free path queries

Many graph query languages use, at their core, path queries that yield node pairs (m,n) that are connected by a path of interest. For the end-user, such node pairs only give limited insight as to why this result is obtained, as the pair does not directly identify the underlying path of interest.In this paper, we propose the single-path semantics to address this limitation of path queries. Under single-path semantics, path queries evaluate to a single path connecting nodes m and n and that satisfies the conditions of the query. To put our proposal in practice, we provide an efficient algorithm for evaluating context-free path queries using the single-path semantics. Additionally, we perform a short evaluation of our techniques that shows that the single-path semantics is practically feasible, even when query results grow large.In addition, we explore the formal relationship between the single-path semantics we propose the problem of finding the shortest string in the intersection of a regular language (representing a graph) and a context-free language (representing a path query). As our formal results show, there is a distinction between the complexity of the single-path semantics for queries that use a single edge label and queries that use multiple edge labels: for queries that use a single edge label, the length of the shortest path is linearly upper bounded by the number of nodes in the graph; whereas for queries that use multiple edge labels, the length of the shortest path has a worst-case quadratic lower bound.

Finding meaningful paths in heterogeneous graphs with PathWays

Graphs, and notably RDF graphs, are a prominent way of sharing data. As data usage democratizes, users need help figuring out the useful content of a graph dataset. In particular, journalists with whom we collaborate are interested in identifying, in a graph, the connections between entities, e.g., people, organizations, emails, etc. We present a novel method for exploring data graphs through their data paths connecting Named Entities (NEs, in short); each data path leads to a tabular-looking set of results. NEs are extracted from the data through dedicated Information Extraction modules. Our method builds upon the pre-existing ConnectionLens platform and follow-up work in the Abstra project, which builds simple, visual ER-style summaries of semi-structured data. The contribution of the present work, and its novelty, is twofold. First, we propose a novel analysis of entity-to-entity paths contained in datasets of any nature, and propose a new method for ranking paths, leveraging a novel Information Extraction (IE) module we built on top of ChatGPT. Second, we present an efficient approach to enumerate and compute NE paths, based on an algorithm which automatically recommends sub-paths to materialize, and rewrites the path queries using these subpaths. Our experiments demonstrate the interest of NE paths and the efficiency of our method for computing and ranking them.

Complex-Path: Effective and Efficient Node Ranking with Paths in Billion-Scale Heterogeneous Graphs

Node ranking in heterogeneous graphs, which quantifies the relative importance of nodes, can often be improved by incorporating information from relevant paths. Graph database and heterogeneous graph neural network (HGNN) are two main approaches to better solve this problem. Graph databases support efficient path queries for flexible path types but require manual design to combine results for node ranking. Conversely, current HGNNs can automatically integrate semantic information from multiple linear path types for accurate node ranking. However, our experiments show that they fail to outperform a multi-layer perceptron model that utilizes features extracted from multiple nonlinear conditional paths, which can be handled by graph databases. Therefore, we aim to enable HGNN to take advantage of these path types for better performance. However, HGNNs require a generalized path schema to define the structure of input paths, and incorporating each additional path type will significantly increase the required system memory and sampling time for HGNNs. To address these limitations, we introduce CompNode, a novel framework based on a new unified path schema definition called Complex-path, which is used to describe all the required path types, including nonlinear conditional path types. Then, we design a pre-aggregation method to reduce the required system memory and sampling time by pre-aggregating the same type of complex-path. Furthermore, we develop a model that combines semantic information from all aggregated complex-paths for accurate node ranking. Real-world experiments on identifying top potential high-value customers show CompNode outperforms state-of-the-art HGNNs by 20% in average precision and the previously deployed graph database method by 252% in success rate.

PCSP: Efficiently Answering Label-Constrained Shortest Path Queries in Road Networks

Shortest path queries are ubiquitous in many spatial applications. Existing solutions assign numerical weights to edges and compute the path with the minimum sum of edge weights. However, in practice, the road categories associated with edges (e.g., toll) can make shortest paths undesirable, e.g., they may use unfavorable toll roads. Augmenting each edge with a label to denote its category, we study the Label-Constrained Shortest Path (LCSP) query that finds the shortest path under the constraint that the edge labels along the path should follow a pattern expressed by a formal language. There have been extensive LCSP solutions, but they are either inefficient in query processing or limited to special languages with low expressiveness capacity. In this paper, we propose the index called Partially Constrained Shortest Path (PCSP), which answers each query quickly by concatenating two shortest paths that partially satisfy the constraint and support more general regular languages. We also present pruning techniques that further optimize query efficiency. Experimental comparison with the state-of-the-art index demonstrates the superiority of PCSP. It can answer each LCSP query in around 100 microseconds and runs faster than the best-known solution by up to two orders of magnitude.

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.

Efficient algorithms for reachability and path queries on temporal bipartite graphs

Efficient algorithms for reachability and path queries on temporal bipartite graphs

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.

Distance queries over dynamic interval graphs

We design the first dynamic distance oracles for interval graphs, which are intersection graphs of a set of intervals on the real line, and for proper interval graphs, which are intersection graphs of a set of intervals in which no interval is properly contained in another.For proper interval graphs, we design a linear space data structure which supports distance queries (computing the distance between two query vertices) and vertex insertion or deletion in O(lg⁡n) worst-case time, where n is the number of vertices currently in G. Under incremental (insertion only) or decremental (deletion only) settings in general interval graphs, we design linear space data structures that support distance queries in O(lg⁡n) worst-case time and vertex insertion or deletion in O(lg⁡n) amortized time, where n is the maximum number of vertices in the graph. Under fully dynamic settings in general interval graphs, we design a data structure that represents an interval graph G in O(n) words of space to support distance queries in O(nlg⁡n/S(n)) worst-case time and vertex insertion or deletion in O(S(n)+lg⁡n) worst-case time, where n is the number of vertices currently in G and S(n) is an arbitrary function that satisfies S(n)=Ω(1) and S(n)=O(n). This implies an O(n)-word solution with O(nlg⁡n)-time support for both distance queries and updates. All four data structures can answer shortest path queries by reporting the vertices in the shortest path between two query vertices in O(lg⁡n) worst-case time per vertex.We also study the hardness of supporting distance queries under updates over an intersection graph of 3D axis-aligned line segments, which generalizes our problem to 3D. Finally, we solve the problem of computing the diameter of a dynamic connected interval graph.

Backbone Index and GNN Models for Skyline Path Query Evaluation over Multi-cost Road Networks

Skyline path queries (SPQs) extend skyline queries to multi-dimensional networks, such as multi-cost road networks (MCRNs). Such queries return a set of non-dominated paths between two given network nodes. Despite the existence of extensive works on evaluating different SPQ variants, SPQ evaluation is still very inefficient due to the nonexistence of efficient index structures to support such queries. Existing index building approaches for supporting shortest-path query execution, when directly extended to support SPQs, use an unreasonable amount of space and time to build, making them impractical for processing large graphs. In this paper, we propose a novel index structure, backbone index , and a corresponding index construction method that condenses an initial MCRN to multiple smaller summarized graphs with different granularity. We present efficient approaches to find approximate solutions to SPQs by utilizing the backbone index structure. Furthermore, considering making good use of historical query and query results, we propose two models, S kyline P ath G raph N eural N etwork (SP-GNN) and T ransfer SP-GNN (TSP-GNN), to support effective SPQ processing. Our extensive experiments on real-world large road networks show that the backbone index can support finding meaningful approximate SPQ solutions efficiently. The backbone index can be constructed in a reasonable time, which dramatically outperforms the construction of other types of indexes for road networks. As far as we know, this is the first compact index structure that can support efficient approximate SPQ evaluation on large MCRNs. The results on the SP-GNN and TSP-GNN models also show that both models can help get approximate SPQ answers efficiently.

A Swell Neural Network Algorithm for Solving Time-Varying Path Query Problems with Privacy Protection

In this paper, a swell neural network (SNN) algorithm was proposed for solving time-varying path query (TVPQ) problems with privacy protection with the following goals: (i) querying the K-nearest paths with time limitations in a time-varying scenario, and (ii) protecting private information from neighborhood attacks. The proposed SNN is a network in which the optimal paths can be calculated at the same time with no need for training. For TVPQ, a node is considered a neuron, and time-varying means that an edge has different costs in different time windows. For SNN, the query paths are swell sets from the start to the target within an upper limit. An encrypted index is designed for privacy protection. The evaluation of the efficiency and accuracy of the SNN was carried out based on New York road instances.

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.

Proximity Queries on Point Clouds using Rapid Construction Path Oracle

The prevalence of computer graphics technology boosts the developments of point clouds in recent years, which offer advantages over terrain surfaces (represented by Triangular Irregular Networks, i.e., TINs) in proximity queries, including the shortest path query, the k-Nearest Neighbor (kNN) query and the range query. Since (1) all existing on-the-fly and oracle-based shortest path query algorithms on a TIN are very expensive, (2) all existing on-the-fly shortest path query algorithms on a point cloud are still not efficient, and (3) there are no oracle-based shortest path query algorithms on a point cloud, we propose an efficient (1+ε)-approximate shortest path oracle that answers the shortest path query for a set of Points-Of-Interests (POIs) on the point cloud, which has a good performance (in terms of the oracle construction time, oracle size and shortest path query time) due to the concise information about the pairwise shortest paths between any pair of POIs stored in the oracle. Our oracle can be easily adapted to answering the shortest path query for any points on the point cloud if POIs are not given as input, and also achieve a good performance. Then, we propose efficient algorithms for answering the (1+ε)-approximate kNN and range query with the assistance of our oracle. Our experimental results show that when POIs are given (resp. not given) as input, our oracle is up to 390 times, 30 times and 6 times (resp. 500 times, 140 times and 50 times) better than the best-known oracle on a TIN in terms of the oracle construction time, oracle size and shortest path query time, respectively. Our algorithms for the other two proximity queries are both up to 100 times faster than the best-known algorithms.

Efficient Regular Simple Path Queries under Transitive Restricted Expressions

Efficient Regular Simple Path Queries under Transitive Restricted Expressions

Temporal Paths in Real-World Sensor Networks

Sensor networks are used in an increasing number and variety of application areas, like traffic control or river monitoring. Sensors in these networks measure parameters of interest defined by domain experts and send these measurements to a central location for storage, viewing and analysis. Temporal graph data models, whose nodes contain time-series data reported by the sensors, have been proposed to model and analyze these networks in order to take informed and timely decisions on their operation. Temporal paths are first-class citizens in this model and some classes of them have been identified in the literature. Queries aimed at finding these paths are denoted as (temporal) path queries. In spite of these efforts, many interesting problems remain open and, in this work, we aim at answering some of them. More concretely, we characterize the classes of temporal paths that can be defined in a sensor network in terms of the well-known Allen’s temporal algebra. We also show that, out of the 8192 possible interval relations in this algebra, only 11 satisfy two desirable properties that we define: transitivity and robustness. We show how these properties and the paths that satisfy them are relevant in practice by means of a real-world use case consisting of an analysis of salinity that appears close to the Scheldt river in Flanders, Belgium, during high tides occurring in the North Sea.

Answering Min-Max Resource-Constrained Shortest Path Queries over Large Graphs

Answering Min-Max Resource-Constrained Shortest Path Queries over Large Graphs

Multi-Source Shortest Path Query With Assembly Points on Large Graphs

Multi-Source Shortest Path Query With Assembly Points on Large Graphs

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.

Label-constrained shortest path query processing on road networks

Label-constrained shortest path query processing on road networks

TOWARDS PEDESTRIAN ACCESSIBILITY ANALYSIS IN INDOOR ENVIRONMENTS WITH CROWDS

Abstract. Except in emergency cases, indoor crowds could also decrease the walking speed of pedestrians in daily life. To investigate daily-based accessibility of locations to a pedestrian in the presence of crowds, this paper proposes a method of indoor accessibility analysis. We adopt a hierarchical spatial model to represent indoor environments and evaluate the varied accessibility to a user. The first level refers to a door network representing door connectivity. On the second level, spaces are gridified so that crowd density can be readily measured, and its obstruction to pedestrians can be quantified at different time slots. Instead of generating specific obstacle-avoidance paths in a short period, we depict accessibility variation with two types of paths, i.e., central and periphery paths inside rooms. Based on the hierarchical model, pathways are pre-computed between doors for a user and indexed in the grid model. In a path query, a sequence of doors is derived from the door network, and the pre-computed pathways are readily retrieved to form the two types of paths. Accordingly, walking time can be estimated with crowd density in these grids at each time slot. We conducted an initial test on a building floor to demonstrate the use of the proposed method. We sampled the locations of simulated crowds (50 persons) every 10 seconds, and the time cost between given doors in both paths are compared. A slowdown occurred in the central path, and the periphery path involves the minimum time in the test scenario. In the future, the relationship between crowd density and the possibility of blockage to pedestrians will be further investigated.

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.