Efficient Algorithm for Constructing Order K Voronoi Diagrams in Road Networks

Efficient algorithm for finding k shortest paths based on re-optimization technique

The problem of identifying the shortest path along a road network is a fundamental problem in network analysis, ranging from route guidance in a navigation system to solving spatial allocation problems. Since this type of problem is solved so frequently, it is important to craft an approach that is as efficient as possible. Based upon past research, it is generally accepted that several efficient implementations of the Dijkstra algorithm are the fastest at optimally solving the ‘one‐to‐one’ shortest path problem (Cherkassky et al.1996). We show that the most efficient state‐of‐the‐art implementations of Dijkstra can be improved by taking advantage of network properties associated with GIS‐sourced data. The results of this paper, derived from tests of different algorithmic approaches on real road networks, will be extremely valuable for application developers and researchers in the GIS community.

It is shown that the order-k Voronoi diagram of n sites with additive weights in the plane has at most (4kź2)(nźk) vertices, (6kź3)(nźk) edges, and (2kź1)(nźitk) + 1 regions. These bounds are approximately the same as the ones known for unweighted order-k Voronoi diagrams. Furthermore, tight upper bounds on the number of edges and vertices are given for the case that every weighted site has a nonempty region in the order-1 diagram. The proof is based on a new algorithm for the construction of these diagrams which generalizes a plane-sweep algorithm for order-1 diagrams developed by Steven Fortune. The new algorithm has time-complexityO(k2n logn) and space-complexityO(kn). It is the only nontrivial algorithm known for constructing order-kc Voronoi diagrams of sites withadditive weights. It is fairly simple and of practical interest also in the special case of unweighted sites.

A comparison of algorithms for origin–destination matrix generation on real road networks and an approximation approach

Path queries such as finding the shortest path in travel time from my hotel to the are heavily used in many applications of road networks. Currently, simple statistic aggregates such as the average travel time between two vertices are often used to answer path queries. However, such simple aggregates often cannot capture the uncertainty inherent in traffic. In this paper, we study how to take traffic uncertainty into account in answering path queries in road networks. To capture the uncertainty in traffic such as the travel time between two vertices, the weight of an edge is modeled as a random variable and is approximated by a set of samples. We propose three novel types of probabilistic path queries using basic probability principles: (1) a probabilistic path query like what are the paths from my hotel to the airport whose travel time is at most 30 minutes with a probability of at least 90%?; (2) a weight-threshold top-k path query like what are the top-3 paths from my hotel to the airport with the highest probabilities to take at most 30 minutes?; and (3) a probability-threshold top-k path query like what are the top-3 shortest paths from my hotel to the airport whose travel time is guaranteed by a probability of at least 90%? To evaluate probabilistic path queries efficiently, we develop three efficient probability calculation methods: an exact algorithm, a constant factor approximation method and a sampling based approach. Moreover, we devise the P* algorithm, a best-first search method based on a novel hierarchical partition tree index and three effective heuristic evaluation functions. An extensive empirical study using real road networks and synthetic data sets shows the effectiveness of the proposed path queries and the efficiency of the query evaluation methods.

Shortest path queries on road networks are widely used in location-based services (LBS), e.g., finding the shortest route from my home to the airport through Google Maps. However, when there are a large number of path queries arrived concurrently or in a short while, an LBS provider (e.g., Google Maps) has to endure a high workload and then may lead to a long response time to users. Therefore, path caching services are utilized to accelerate large-scale path query processing, which try to store the historical path results and reuse them to answer the coming queries directly. However, most of existing path caches are organized based on nodes of paths; hence, the underlying road network topology is still needed to answer a path query when its querying origin or destination lies on edges. To overcome this limitation, we propose an edge-based shortest path cache in this paper that can efficiently handle queries without needing any road information, which is much more practical in the real world. We achieve this by designing a totally new edge-based path cache structure, an efficient R-tree-based cache lookup algorithm, and a greedy-based cache construction algorithm. Extensive experiments on a real road network and real point-of-interest datasets are conducted, and the results show the efficiency, scalability, and applicability of our proposed caching techniques.

On road networks, the clustering of moving objects is important for traffic monitoring and routes recommendation. The existing schemes find out density route by considering the number of vehicles in a road segment. Since they don’t consider the features of each road segment such as width, length, and directions in a road network, the results are not correct in some real road networks. To overcome such problems, we propose a clustering method for congested routes discovering from the trajectories of moving objects on road networks. The proposed scheme can be divided into three steps. First, it divides each road network into segments with different width, length, and directions. Second, the congested road segments are detected through analyzing the trajectories of moving objects on the road network. The saturation degree of each road segment and the average moving speed of vehicles in a road segment are computed to detect the congested road segments. Finally, we compute the final congested routes by using a clustering scheme. The experimental results showed that the proposed scheme can efficiently discover the congested routes in different directions of the roads.

At present, the urban traffic system is faced with the problems of congestion and low efficiency, and the traditional methods have certain limitations when dealing with the complex urban road network. This paper aims to explore a new method of capacity Optimization of Road Networks in a Smart City environment and proposes a method based on a Graph Neural network, named “Smart City Road optimization Graph Neural Network” (SCRO-GNN). SCRO-GNN first collects and preprocesses multi-source data, including road network data, traffic flow, accident records, environmental factors, etc. The key node and edge features, including the number of lanes at the intersection, the traffic flow of the section, and the adjacency matrix of the road network are defined to characterize the structure of the road network. Then, the graph neural network model is constructed and trained to predict the traffic flow of different sections and evaluate the road capacity by using the graph structure of the road network. This paper tests the performance of SCRO-GNN on real road networks in multiple cities. The results show that, compared with the traditional traffic flow prediction model, SCRO-GNN can significantly improve the prediction accuracy, especially when dealing with the highly complex urban road network structure. Based on these predictions, the proposed optimization strategy performed well in reducing traffic congestion and improving the efficiency of road use. The research in this paper not only demonstrates the potential of graph neural networks in smart city road network optimization, but also provides a new direction for future traffic system research. The successful implementation of the SCRO-GNN approach is expected to provide more efficient and intelligent solutions for urban traffic management and planning.

Efficient fastest path computation on a large scale road network is an essential problem in logistics distribution, especially based on real-time traffic information. In this paper, we present an adaptive fastest path algorithm capable of efficiently accounting for the network with real-time traffic data. (1) Logistics vehicle routing between two cities usually choose the road network through the largest roads. According to this traveler character and the natural hierarchy present in road network, we classify the roads into largest roads and smaller ones. (2) Based on the largest roads and smaller roads, we can partition the road network into areas. (3) Finally, we propose an efficient A* algorithm that uses the road network partition to limit the search space and considers the real-time traffic information. Through an extensive experimental evaluation on real road network we show that our algorithm provides desirable routes, and that it is significantly fast and effective.

Chapter 5 - Voronoi Diagrams

Network Voronoi Diagram on uncertain objects for nearest neighbor queries

Chapter 20 - Voronoi Diagram Distances

In this paper, we consider a new problem in the context of road network databases, named Resource Constrained Best Upgrade Plan computation (BUP, for short). Consider a transportation network (weighted graph) G where a subset of the edges are upgradable, i.e., for each such edge there is a cost, which if spent, the weight of the edge can be reduced to a specific new value. Given a source and a destination in G, and a budget (resource constraint) B, the BUP problem is to identify which upgradable edges should be upgraded so that the shortest path distance between source and destination (in the updated network) is minimized, without exceeding the available budget for the upgrade. In addition to transportation networks, the BUP query arises in other domains too, such as telecommunications. We propose a framework for BUP processing and evaluate it with experiments on large, real road networks.

In this paper, we study the problem of searching k-discriminative paths on road networks. Given a source node src and a destination node dest on a road network, we aim to search k paths between src and dest, where these k paths satisfy the multi-objective goal including the minimization of the path overlapping and the minimization of the path length. Specifically, the requirement of minimizing the overlapping among paths, which is a NP-hard issue, is highly demanded in applications of disaster rescue management such as the evacuation plan. In this paper, we consider the deployment of k-discriminative paths for various applications, including queries for emergency-purpose applications, queries of multi-objective Pareto front for pre-schedule transportation plan, and queries with multiple sources and destinations for the regional evacuation. Due to its NP-hard nature, the heuristic strategy based on the ant colony optimization is devised in this work. As validated by our experimental studies on real road networks, the proposed algorithm can achieve the discovery of k-discriminative paths efficiently and effectively, showing its prominent advantages to be a practicable service for evacuation-related applications.

Integrating heterogeneous spatial data is a crucial problem for geographical information systems (GIS) applications. Previous studies mainly focus on the matching of heterogeneous road networks or heterogeneous polygonal data sets. Few literatures attempt to approach the problem of integrating the point of interest (POI) from volunteered geographic information (VGI) and professional road networks from official mapping agencies. Hence, the article proposes an approach for integrating VGI POIs and professional road networks. The proposed method first generates a POI connectivity graph by mining the linear cluster patterns from POIs. Secondly, the matching nodes between the POI connectivity graph and the associated road network are fulfilled by probabilistic relaxation and refined by a vector median filtering (VMF). Finally, POIs are aligned to the road network by an affine transformation according to the matching nodes. Experiments demonstrate that the proposed method integrates both the POIs from VGI and the POIs from official mapping agencies with the associated road networks effectively and validly, providing a promising solution for enriching professional road networks by integrating VGI POIs.