Path Queries Research Articles

Probabilistic Time-Constrained Paths Search over Uncertain Road Networks

With the proliferation of positioning technologies and GPS-enabled mobile devices, it has become very important to search for optimal paths to cover required points of interest (POIs, e.g., banks and restaurants) over road networks in many location-based services. In practice, however, traffic conditions are inherently uncertain and dynamically changing over time, which makes it rather challenging to provide accurate results for path queries based on travelling time. Inspired by this, we consider the practical settings of road networks and model them by uncertain road networks (URNs) on which the travelling time of each road is uncertain and captured by a set of travelling time samples. Then, we formalize the probabilistic time-constrained path ( PTP ) query over uncertain road networks to retrieve those paths that not only cover required POIs with constrained service time but also have the minimum travelling times in high confidence. We prove that PTP query problem is NP-hard. In order to answer PTP queries efficiently, we propose an efficient PTP query approach with effective pruning strategies regarding the time constraints on POIs and the probabilistic/rank requirements of queries. Extensive experiments on real road networks validate the efficiency and effectiveness of our PTP query approach.

Enhancing social network privacy with accumulated non-zero prior knowledge

With the fast development of social networks, privacy protection on social network data has already attracted more and more research attention. If an adversary has collected enough information by intentionally querying a social network, the privacy of social network data might be successfully inferred based on the previous query results, which is seldom investigated by most existing approaches. In this paper, we first formulate the correlated query results as the non-zero prior knowledge, then propose a novel differential privacy approach to enhance privacy of social network data from being inferred. The corresponding ϵ-difference is re-formulated as well as the calculation of the sensitivity between two “neighboring” social graphs. Particularly, the calculation of sensitivity is proposed for three widely adopted queries on social networks, i.e., node degree distribution query, cut set query and the shortest path query. To evaluate our approach, rigorous experiments have been performed on three real world data sets. The promising experimental results have demonstrated that the proposed approach is superior to the state-of-the-art privacy protection approaches with respect to data privacy and data utility.

Accurate and fast path computation on large urban road networks: A general approach.

Accurate and fast path computation is essential for applications such as onboard navigation systems and traffic network routing. While a number of heuristic algorithms have been developed in the past few years for faster path queries, the accuracy of them are always far below satisfying. In this paper, we first develop an agglomerative graph partitioning method for generating high balanced traverse distance partitions, and we constitute a three-level graph model based on the graph partition scheme for structuring the urban road network. Then, we propose a new hierarchical path computation algorithm, which benefits from the hierarchical graph model and utilizes a region pruning strategy to significantly reduce the search space without compromising the accuracy. Finally, we present a detailed experimental evaluation on the real urban road network of New York City, and the experimental results demonstrate the effectiveness of the proposed approach to generate optimal fast paths and to facilitate real-time routing applications.

Dynamic Path Queries in Linear Space

In the path reporting problem, we preprocess a tree on n nodes each of which is assigned a weight, such that given an arbitrary path and a weight range, we can report the nodes whose weights are within the range. We consider this problem in dynamic settings, and propose the first non-trivial linear-space solution that supports path reporting in $$O((\lg n{/}\lg \lg n)^2 + occ \lg n{/}\lg \lg n)$$ time, where occ is the output size, and the insertion and deletion of a node of an arbitrary degree in $$O(\lg ^{2+\epsilon } n)$$ amortized time, for any constant $$\epsilon \in (0, 1)$$ . Obvious solutions based on directly dynamizing solutions to the static version of this problem all require $$\Omega ((\lg n{/}\lg \lg n)^2)$$ time for each node reported, and thus our query time is much faster. We also design data structures that support path counting and path reporting queries in $$O((\lg n{/}\lg \lg n)^2)$$ time, and insertions and deletions in $$O((\lg n{/}\lg \lg n)^2)$$ amortized time. This matches the best known results for dynamic two-dimensional range counting (He and Munro in Comput Geom 47(2):268–281, 2014) and range selection (He et al., in: Proceedings of the 22nd international symposium on algorithms and computation, ISAAC, Yokohama, Japan, 2011), which can be viewed as special cases of path counting and path selection.

Синтаксический анализ графов с использованием конъюнктивных грамматик

Graphs are used as a data structure to represent large volumes of information in a compact and convenient for analysis form in many areas: bioinformatics, graph databases, static code analysis, etc. In these areas, it is necessary to evaluate a queries for large graphs in order to determine the dependencies between the nodes. The answer to such queries is usually a set of all triples (A, m, n) for which there is a path in the graph from the vertex m to the vertex n, such that the labels on the edges of this path form a string derivable from the nonterminal A in some context-free grammar. This type of query is calculated using relational query semantics and context-free grammars but there are conjunctive grammars, which form a broader class of grammars than traditional context-free grammars. The use of conjunctive grammars in the path querying allows us to formulate more complex queries to the graph and solve a wider class of problems. It is known that the path querying using relational query semantics and conjunctive grammars is undecidable problem. In this paper, we propose a path querying algorithm which uses relational query semantics and conjunctive grammars, and approximates the exact solution. The proposed algorithm is based on matrix operations, and our evaluation shows that it is possible to significantly improve the performance of the algorithm by using a graphics processing unit.

PACE: a PAth-CEntric paradigm for stochastic path finding

With the growing volumes of vehicle trajectory data, it becomes increasingly possible to capture time-varying and uncertain travel costs, e.g., travel time, in a road network. The current paradigm for doing so is edge-centric: it represents a road network as a weighted graph and splits trajectories into small fragments that fit the underlying edges to assign time-varying and uncertain weights to edges. It then applies path finding algorithms to the resulting, weighted graph. We propose a new PAth-CEntric paradigm, PACE, that targets more accurate and more efficient path cost estimation and path finding. By assigning weights to paths, PACE avoids splitting trajectories into small fragments. We solve two fundamental problems to establish the PACE paradigm: (i) how to compute accurately the travel cost distribution of a path and (ii) how to conduct path finding for a source–destination pair. To solve the first problem, given a departure time and a query path, we show how to select an optimal set of paths that cover the query path and such that the weights of the paths enable the most accurate joint cost distribution estimation for the query path. The joint cost distribution models well the travel cost dependencies among the edges in the query path, which in turn enables accurate estimation of the cost distribution of the query path. We solve the second problem by showing that the resulting path cost distribution estimation method satisfies an incremental property that enables the method to be integrated seamlessly into existing stochastic path finding algorithms. Further, we propose a new stochastic path finding algorithm that fully explores the improved accuracy and efficiency provided by PACE. Empirical studies with trajectory data from two different cities offer insight into the design properties of the PACE paradigm and offer evidence that PACE is accurate, efficient, and effective in real-world settings.

Hybrid Spatial Data Model for Indoor Space: Combined Topology and Grid

The construction and application of an indoor spatial data model is an important prerequisite to meet the requirements of diversified indoor spatial location services. The traditional indoor spatial topology model focuses on the construction of topology information. It has high path analysis and query efficiency, but ignores the spatial location information. The grid model retains the plane position information by grid, but increases the data volume and complexity of the model and reduces the efficiency of the model analysis. This paper presents a hybrid model for interior space based on topology and grid. Based on the spatial meshing and spatial division of the interior space, the model retains the position information and topological connectivity information of the interior space by establishing the connection or affiliation between the grid subspace and the topological subspace. The model improves the speed of interior spatial analysis and solves the problem of the topology information and location information updates not being synchronized. In this study, the A* shortest path query efficiency of typical daily indoor activities under the grid model and the hybrid model were compared for the indoor plane of an apartment and a shopping mall. The results obtained show that the hybrid model is 43% higher than the A* algorithm of the grid model as a result of the existence of topology communication information. This paper provides a useful idea for the establishment of a highly efficient and highly available interior spatial data model.

Data Access Based on a Guide Map of the Underwater Wireless Sensor Network.

Underwater wireless sensor networks (UWSNs) represent an area of increasing research interest, as data storage, discovery, and query of UWSNs are always challenging issues. In this paper, a data access based on a guide map (DAGM) method is proposed for UWSNs. In DAGM, the metadata describes the abstracts of data content and the storage location. The center ring is composed of nodes according to the shortest average data query path in the network in order to store the metadata, and the data guide map organizes, diffuses and synchronizes the metadata in the center ring, providing the most time-saving and energy-efficient data query service for the user. For this method, firstly the data is stored in the UWSN. The storage node is determined, the data is transmitted from the sensor node (data generation source) to the storage node, and the metadata is generated for it. Then, the metadata is sent to the center ring node that is the nearest to the storage node and the data guide map organizes the metadata, diffusing and synchronizing it to the other center ring nodes. Finally, when there is query data in any user node, the data guide map will select a center ring node nearest to the user to process the query sentence, and based on the shortest transmission delay and lowest energy consumption, data transmission routing is generated according to the storage location abstract in the metadata. Hence, specific application data transmission from the storage node to the user is completed. The simulation results demonstrate that DAGM has advantages with respect to data access time and network energy consumption.

Energy-efficient air-indices for shortest path and distance queries on road networks

Although various air-indices, e.g., Next Region (NR), have been proposed to support shortest path and distance queries at mobile clients on a road network, how to minimize the energy cost, which is dominated by the cost for obtaining traffic data from data broadcast, is still one of the most important performance objectives. Inspired by various preprocessing schemes in traditional computation models for shortest path queries that make use of special properties of road networks, we design in this paper a new air-index called the CH Index with the purpose of minimizing the energy cost for obtaining broadcasting data to perform shortest path and distance queries at mobile clients. Experimental evaluation shows that our CH Index is more energy efficient than the state-of-the-art index NR by an order of magnitude. We also extend the CH Index to the CHBN Index which provides a tradeoff between energy efficiency and response time for obtaining traffic data via a user-tunable parameter. We show that CHBN gives shorter response time than CH while still being energy efficient.

Privacy Preserving in Cloud Environment for Obstructed Shortest Path Query

With the prosperity of location-based services, shortest path query became one of the most common services, and provided convenience for finding the best way to arrive at the destination of users. However, in order to obtain the service, users had to submit the current locations to a data owner, and this process may pose privacy threats to users. More seriously, if the data owner outsourcing the query data to a cloud server for calculating the shortest distance, users’ privacy may be leaked even further. To cope with the problem of outsourcing computation, based the homomorphic encryption and secure multiparty computation, this manuscript presents a framework to reduce the likelihood of private information leakage, and privacy preservation of both the user, and the data owner. In this framework, two different conditions were considered, and the shortest path was computed with or without obstruction on the road. Thereafter, two protocols called “query with obstruction” and “query without obstruction” are presented.

Minimal on-road time route scheduling on time-dependent graphs

On time-dependent graphs, fastest path query is an important problem and has been well studied. It focuses on minimizing the total travel time (waiting time + on-road time) but does not allow waiting on any intermediate vertex if the FIFO property is applied. However, in practice, waiting on a vertex can reduce the time spent on the road (for example, resuming traveling after a traffic jam). In this paper, we study how to find a path with the minimal on-road time on time-dependent graphs by allowing waiting on some predefined parking vertices. The existing works are based on the following fact: the arrival time of a vertex v is determined by the arrival time of its in-neighbor u , which does not hold in our scenario since we also consider the waiting time on u if u allows waiting. Thus, determining the waiting time on each parking vertex to achieve the minimal on-road time becomes a big challenge, which further breaks FIFO property. To cope with this challenging problem, we propose two efficient algorithms using minimum on-road travel cost function to answer the query. The evaluations on multiple real-world time-dependent graphs show that the proposed algorithms are more accurate and efficient than the extensions of existing algorithms. In addition, the results further indicate, if the parking facilities are enabled in the route scheduling algorithms, the on-road time will reduce significantly compared to the fastest path algorithms.

Shrink: Distance preserving graph compression

The ever increasing size of graphs makes them difficult to query and store. In this paper, we present Shrink, a compression method that reduces the size of the graph while preserving the distances between the nodes. The compression is based on the iterative merging of the nodes. During each merging, a system of linear equations is solved to define new edge weights in a way that the new weights have the least effect on the distances. Merging nodes continues until the desired size for the compressed graph is reached. The compressed graph, also known as the coarse graph, can be queried without decompression. As the complexity of distance-based queries such as shortest path queries is highly dependent on the size of the graph, Shrink improves the performance in terms of time and storage. Shrink not only provides the length of the shortest path but also identifies the nodes on the path. The approach has been applied to both weighted and unweighted graphs including road network, friendship network, collaboration network, web graph and social network. In the experiment, a road network with more than 2.5 million nodes is reduced to fifth while the average relative error is less than 1%.

Efficient processing of shortest path queries in evolving graph sequences

In many applications, information is best represented as graphs. In a dynamic world, information changes and so the graphs representing the information evolve with time. We propose that historical graph-structured data be maintained for analytical processing. We call a historical evolving graph sequence an EGS. We observe that in many applications, graphs of an EGS are large and numerous, and they often exhibit much redundancy among them. We study the problem of efficient shortest path query processing on an EGS and put forward a solution framework called FVF. Two algorithms, namely, FVF-F and FVF-H, are proposed. While the FVF-F algorithm works on a sequence of flat graph clusters, the FVF-H algorithm works on a hierarchy of such clusters. Through extensive experiments on both real and synthetic datasets, we show that our FVF framework is highly efficient in shortest query processing on EGSs. Comparing FVF-F and FVF-H, the latter gives a larger speedup, is more flexible in terms of memory requirements, and is far less sensitive to parameter values.

TAPER: query-aware, partition-enhancement for large, heterogenous graphs

Graph partitioning has long been seen as a viable approach to addressing Graph DBMS scalability. A partitioning, however, may introduce extra query processing latency unless it is sensitive to a specific query workload, and optimised to minimise inter-partition traversals for that workload. Additionally, it should also be possible to incrementally adjust the partitioning in reaction to changes in the graph topology, the query workload, or both. Because of their complexity, current partitioning algorithms fall short of one or both of these requirements, as they are designed for offline use and as one-off operations. The TAPER system aims to address both requirements, whilst leveraging existing partitioning algorithms. TAPER takes any given initial partitioning as a starting point, and iteratively adjusts it by swapping chosen vertices across partitions, heuristically reducing the probability of inter-partition traversals for a given path queries workload. Iterations are inexpensive thanks to time and space optimisations in the underlying support data structures. We evaluate TAPER on two different large test graphs and over realistic query workloads. Our results indicate that, given a hash-based partitioning, TAPER reduces the number of inter-partition traversals by sim 80%; given an unweighted Metis partitioning, by sim 30%. These reductions are achieved within eight iterations and with the additional advantage of being workload-aware and usable online.

GMark: Schema-Driven Generation of Graphs and Queries

Massive graph data sets are pervasive in contemporary application domains. Hence, graph database systems are becoming increasingly important. In the experimental study of these systems, it is vital that the research community has shared solutions for the generation of database instances and query workloads having predictable and controllable properties. In this paper, we present the design and engineering principles of gMark, a domain- and query language-independent graph instance and query workload generator. A core contribution of gMark is its ability to target and control the diversity of properties of both the generated instances and the generated workloads coupled to these instances. Further novelties include support for regular path queries, a fundamental graph query paradigm, and schema-driven selectivity estimation of queries, a key feature in controlling workload chokepoints. We illustrate the flexibility and practical usability of gMark by showcasing the framework's capabilities in generating high quality graphs and workloads, and its ability to encode user-defined schemas across a variety of application domains.

Distributed shortest path query processing on dynamic road networks

Shortest path query processing on dynamic road networks is a fundamental component for real-time navigation systems. In the face of an enormous volume of customer demand from Uber and similar apps, it is desirable to study distributed shortest path query processing that can be deployed on elastic and fault-tolerant cloud platforms. In this paper, we combine the merits of distributed streaming computing systems and lightweight indexing to build an efficient shortest path query processing engine on top of Yahoo S4. We propose two types of asynchronous communication algorithms for early termination. One is first-in-first-out message propagation with certain optimizations, and the other is prioritized message propagation with the help of navigational intelligence. Extensive experiments were conducted on large-scale real road networks, and the results show that the query efficiency of our methods can meet the real-time requirement and is superior to Pregel and Pregel+. The source code of our system is publicly available at https://github.com/yangdingyu/cands.

Flexible query processing for SPARQL

Flexible querying techniques can enhance users’ access to complex, heterogeneous datasets in settings such as Linked Data, where the user may not always know how a query should be formulated in order to retrieve the desired answers. This paper presents query processing algorithms for a fragment of SPARQL 1.1 incorporating regular path queries (property path queries), extended with query approximation and relaxation operators. Our flexible query processing approach is based on query rewriting and returns answers incrementally according to their “distance” from the exact form of the query. We formally show the soundness, completeness and termination properties of our query rewriting algorithm. We also present empirical results that show promising query processing performance for the extended language.

Mathematical programming model and algorithm for time-varying transit network

The shortest path query problem in large scale time-varying transit network is NPhard.Approximate search algorithm is not satisfactory,and the exact search algorithm is inefficient.In this paper,a time-varying mathematical model for transit network is formulated according to the time-varying and uncertainty characteristic of public transport network.The choice of the optimal path for transit network is decomposed into transfer times and transfer line query problem.A query algorithm for transfer times is proposed based on the line mapping network and an algorithm for both transfer site and travel distance is proposed based on site mapping network.Both of them are polynomial.Finally we use a numerical example to illustrate the solution process of the proposed method.

Efficient evaluation of shortest travel-time path queries through spatial mashups

In the real world, the route/path with the shortest travel time in a road network is more meaningful than that with the shortest network distance for location-based services (LBS). However, not every LBS provider has adequate resources to compute/estimate travel time for routes by themselves. A cost-effective way for LBS providers to estimate travel time for routes is to issue external route requests to Web mapping services (e.g., Google Maps, Bing Maps, and MapQuest Maps). Due to the high cost of processing such external route requests and the usage limits of Web mapping services, we take the advantage of direction sharing, parallel requesting and waypoints supported by Web mapping services to reduce the number of external route requests and the query response time for shortest travel-time route queries in this paper. We first give the definition of sharing ability to reflect the possibility of sharing the direction information of a route with others, and find out the queries that their query routes are independent with each other for parallel processing. Then, we model the problem of selecting the optimal waypoints for an external route request as finding the longest simple path in a weighted complete digraph. As it is a MAX SNP-hard problem, we propose a greedy algorithm with performance guarantee to find the best set of waypoints in an external route request. We evaluate the performance of our approach using a real Web mapping service, a real road network, real and synthetic data sets. Experimental results show the efficiency, scalability, and applicability of our approach.

Efficient Path Query Processing Through Cloud-Based Mapping Services

Shortest path queries have been widely used in location-based services (LBSs). To calculate the shortest path from an origin to a destination, an LBS provider usually needs to know the map data of the underlying road network, which can be rather costly especially if such data need to be kept continuously and up to date. A cost-effective way is that LBS providers outsource the shortest path query processing to cloud-based mapping services such as Google Maps, by retrieving the detailed path information from them through external requests. Due to the high cost of accessing data through external requests and the usage limits of mapping services, we propose two optimization techniques in this paper, namely, path sharing and path caching, to reduce the number of external requests and the user query response time. Unlike previous work where the underlying road network is given, this paper optimizes path query processing only based on query origins and destinations. The basic idea of path sharing optimization is that the path information of a query can be shared with another query $q$ if $q$ values origin and destination both lie on the path. To achieve this, we propose an effective method to compute whether or not a query origin/destination lies on a path only based on the Euclidean distance between them. Path caching, an extension of path sharing, lets an LBS provider answer path queries directly based on cached paths. To accomplish this, we first formulate the problem of constructing path cache as a knapsack problem and design a greedy algorithm to solve it; then, we devise an effective cache structure to support efficient cache lookup. Extensive experiments on Bing Maps and real data sets are conducted, and the results show the efficiency, scalability, and applicability of our proposed approaches.