Mathematical Problems in Engineering

Volume 2018, Article ID 6749650, 14 pages

https://doi.org/10.1155/2018/6749650

## Supporting Continuous Skyline Queries in Dynamically Weighted Road Networks

^{1}Management School, University of Shanghai for Science and Technology, Shanghai, China^{2}Academic Affairs Section, Shanghai University of International Business and Economics, Shanghai, China

Correspondence should be addressed to Yingfeng Tang; moc.nuyila@3891fygnat

Received 21 April 2018; Revised 2 August 2018; Accepted 16 August 2018; Published 10 September 2018

Academic Editor: Mahmoud Mesbah

Copyright © 2018 Yingfeng Tang and Shiping Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The paper focuses on the design of an optimum method for handling the continuous skyline query problem in road networks. Existing studies on processing the continuous skyline query focus exclusively on static road networks, which are limited because the state of roads in road networks is constantly changing. Therefore, to apply current methods for dynamically weighted road networks, a distributed skyline query method based on a grid partition method has been proposed in this paper. The method adopts the concepts of a distributed computing framework and road network preprocessing computations in which multiple parallel computing nodes are allocated and organized in grids. Using this approach, the road network map is simplified to a hub graph with much smaller scale such that the query load of the central node can be significantly reduced. The theoretical analysis and experimental results both indicate that, by using the proposed method, the system can achieve quick response time for users as well as a good balance between response times and accuracy. Therefore, it can be concluded that using the proposed method is beneficial for handling continuous skyline queries in a dynamically weighted road network.

#### 1. Introduction

Providing location-based services (LBSs) [1] for moving objects in road networks has become an important research topic in traffic informatization and intelligent traffic system development [2] due to the advances in wireless communication and global positioning system (GPS) technologies. Recommendation systems for moving objects have become an increasingly popular function for road networks, for example, for recommending hotels, car parks, and taxi services based on the real-time locations of network users. In recent years, in conjunction with the development of numerous databases, the skyline query [3] has become an important method to solve LBSs for road networks and moving object recommendation systems. One example of the application may be that a moving object set is used to query taxis preferred by users, i.e., cars in good conditions, drivers with long service records, good ratings, and close proximity to a user’s location. To achieve this, skyline can be used to conduct queries based on the user’s criteria. Results are then presented to the user and they will be asked to make a decision.

The skyline query was first introduced into the database domain in 2001 by Borzsonyi et al., who proposed two basic skyline query algorithms which are block nested loops and divide and conquer (D&C) [3]. Since then, researchers have improved these algorithms and extensively studied skyline queries in a wide variety of scenarios [4–8]. With the continued expansion and development of wireless communication and mobile location technologies, the demand for LBSs has motivated researchers to extend skyline queries to various mobile computing scenarios. Sharifzadeh et al. first proposed the concept of a spatial skyline query [9], and then Deng et al. extended spatial skyline queries to road network scenarios [10]. In [10], Deng et al. measured the distance between the user and interested object as an attribute of the interested object and proposed a multisource skyline query in road networks. To this end, they introduced three algorithms which are collaborative expansion (CE), Euclidean distance constraint (EDC), and lower bound constraint (LBC). More specifically, CE finds the next nearest neighbor for all query points. Further, EDC first calculates Euclidean distances for all data points and then runs a Euclidean skyline algorithm to output the skyline points, with those points serving as the initial candidate set of the skyline point. Finally, LBC is the same as CE, but LBC uses various optimization techniques, e.g., Euclidean distance computation is used to save network distance calculation. In 2008, Frankenstein et al. studied the continuous skyline query problem of moving objects in road networks [11] and proposed a method that processes a continuous skyline through precomputed shortest range data for targets.

More recently, researchers have studied the continuous skyline query problem of moving objects in road networks from a variety of perspectives. In [12], Huang et al. used a grid structure to index the road network and moving object information to improve the access efficiency of road network data, directly calculating the shortest path between objects using Dijkstra’s algorithm. In [13], Shekelyan presented a method for computing a linear path skyline to simplify the query result set, using the multi-Dijkstra algorithm to continuously update the shortest path information. In [14], Prabha et al. focused on the authentication problem of moving objects in a continuous skyline query process, proposing a system that applies a spatial precomputed approach for continuous skyline query. In [15], Safar et al. filtered candidate interest points by calculating the nearest neighbor of each query point, thereby reducing the query space and the number of required shortest path computations wherein a spatial data structure is used to store precomputed shortest path information between nodes of the road network. In [16], Shi et al. approached continuous skyline queries by focusing on location range, transforming interest point sets into Voronoi units, and reducing query times by preprocessing data from the Voronoi units from within the road network. In [17], Fu et al. studied the continuous skyline query problem involving uncertain moving objects by introducing an uncertainty data model in which shortest path information between objects is updated directly according to each event.

In the skyline query process for road networks, the required computation of shortest path between moving objects occupies the main portion of the calculations. Dijkstra’s algorithm [18] is a representative network shortest path algorithm. The algorithm propagates a search wavefront from a source vertex until a destination vertex is reached. The algorithm [19] is a heuristic method. The key idea of is that if there is only one destination, the wavefront expansion process can be optimized towards the direction of the destination vertex. The two algorithms mentioned above are on-the-fly, that is, directly computing the shortest path without any precomputing. Because of the high computing complexity of path search on large-scale road network, the on-the-fly methods cannot meet the requirement for real-time query. Precomputing methods were used to improve query response time of shortest path. There are some studies [20, 21] on the approach with precomputing transitive closure of graph. This type of approach is not suitable for large road networks, because of the huge storage space requirement. And due to huge cost of precomputing for transitive closure, it is also not suitable for dynamically weighted road networks. In [22], Hu et al. proposed a method that stores and indexes the network distances between every vertex and data object with different level of accuracy according to the distance between them. This approach is also not suitable for dynamically weighted road networks due to the high maintenance cost when the network is updated. Another kind of methods with precomputing is based on hierarchical fashion [23–26]. In these methods, a large graph is divided into smaller subgraphs and organizes them in a hierarchical fashion. For each subgraph, the border vertices are the entrances and only the distances between these border vertices are precomputed. Therefore, while computing the network distance, intermediate vertices inside the subgraph are skipped over. However, hierarchical fashion is not suitable for skyline query, since it often requires computing network distances from one source to several destinations. Thus, it is desirable to keep the distance information for the intermediate vertices.

In practice, there are two key challenges when conducting queries using the skyline-based moving object recommendation approach. First, data of moving object is collected by many sensors distributed throughout the road network. Using a traditional method of centralized data processing, large amounts of resources will be wasted in data transmission, thus causing low efficiency. Second, such a centralized processing approach is inadequate for real-time and on-demand application because of the huge numbers and widely scattered moving object data. Finally, road networks are often dynamic rather than static; therefore, the edge weights usually depend on timing because of traffic congestion and road maintenance work being carried out. In general, it is not possible to rely on any precomputation of road network data for determining an optimum route between vertices. Alternatively, computation must be based on real-time data. However, any computation based on a single point will be inadequate in meeting the real-time requirement because of the vast amount of data acquired from road networks.

Summarizing the existing skyline query methods for road network, there are two ways for calculating the shortest distance between moving objects in the skyline query process. The first approach is on-the-fly, that is, to identify the two objects as two vertices in the road network and then to use a shortest path algorithm (e.g., Dijkstra’s algorithm) to perform direct calculations. This method can also be applied to a dynamically weighted road network, but the required computation rapidly increases as the scale of the road network increases. The second approach is to precompute and store the shortest distance between vertices within the road network. When querying, the shortest distance between two objects can be obtained by querying the shortest distance between the nearest neighbor vertices of each object. This approach results in faster query response times, but it cannot be applied to a dynamically weighted road network because of the huge cost from precomputation. Therefore, in this paper, grid-skyline query (Gsky) is proposed to strike a balance between the above two methods in large-scale dynamically weighted road networks.

Gsky is based on dividing a dynamic road network into small manageable units of grids. Using the proposed method, the entire road network is divided into a finite number of grids with a computing node allocated within each grid. This computing node is responsible for collecting and updating information about all moving objects and maintaining a localized distance for all vertices of each grid. Subsequently, a central node is placed for the entire system. When queries are submitted, the central node will gather the required data of moving object and information of localized distance from relevant computing nodes and compute the distance between the moving objects in real time. Finally, users will receive the updated skyline set from Gsky based on changes in distances between moving objects.

Gsky handles moving object information with distributed computing nodes. Therefore, the central node is only activated when there is a query; also, only the interested moving object will be involved in the computation. By using this approach, we can avoid a large amount of data transmission. Generally, parallel computation is performed by computing nodes to update the distances between local vertices. The required information is then fed to the central node only when there is a query. Therefore, the computing workload of the central node should be significantly reduced and managed. Hence the central node only needs to maintain the topology structure of the grids, thereby reducing data maintenance for the central node.

#### 2. Relevant Models

*Definition 1 (road network). *A road network can be abstractly defined as weighted undirected graph G(V, E, W), where vertex set V denotes all cross-points in the road network, w represents the length of each road with the consideration of traffic congestion, with w *∈* W and w > 0, and E represents all edges. As shown in Figure 1, G is a road network that includes 22 cross-points and 35 edges.