Research on improved bidirectional Dijkstra shortest path based on heap structures

Ride sharing has been widely studied in academia and applied in mobility-on-demand (MoD) systems as a means of reducing the number of cars, congestion, and pollution by sharing empty seats. Solving this problem is challenging on large-scale road networks for the following two reasons: distance calculation on large-scale road networks is time consuming; and multi-request allocation and multi-point planning have been proved to be NP-hard problems. In this paper, we propose a clustering-based request matching and route planning algorithm Roo that considers spatial-temporal distances between ride requests on road networks. The Roo algorithm is evaluated with real-world taxi trajectory data and road networks from New York City and Beijing. The results show that Roo can save up to 50% of mileage by 1000 vehicles serving around 7000 trip requests in New York City between 7:40 am to 8:00 am with average waiting time of 4 minutes.

This paper proposes a parallel shortest path-searching algorithm and implements it on a newly structured parallel reconfigurable processor, DAPDNA-2 (IPFlex Inc). Routing determines the shortest paths from the source to the ultimate destination through intermediate nodes. In open shortest path first (OSPF), Dijkstra's shortest path algorithm, which is the conventional one, finds the shortest paths from the source on a program counter-based processor. The calculation time for Dijkstra's algorithm is O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) when the number of nodes is N. When the network scale is large, calculation time required by Dijkstra's algorithm increases rapidly. It's very difficult to compute Dijkstra's algorithm in parallel because of the need for previous calculation results, so Dijkstra's algorithm is unsuitable for parallel processors. Our proposed scheme finds the shortest paths using a simultaneous multi-path search method. In contrast with Dijkstra's algorithm, several nodes can be determined at one time. Moreover, we partition the network into different groups (network groups) and find the all-node pair's shortest path in each group using a pipeline operation. Networks can be abstracted, and the shortest paths in very large networks can be found easily. The proposed scheme can decrease calculation time from O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) to O(N) using a pipeline operation on DAPDNA-2. Our simulations show that the proposed algorithm uses 99.6% less calculation time than Dijkstra's algorithm. The proposed algorithm can be applied to the very large Internet network designs of the future.

Labeling methods for partially ordered paths

A dynamic spatial–temporal deep learning framework for traffic speed prediction on large-scale road networks

The area rate of the toll road network is designed to influence the regional road network traffic flow configuration and an important factor of goods vehicle path selection, transportation, and other related departments in formulating the related standard. The toll rate is usually combined with the local passenger and cargo loading conditions. Adjusting and optimizing the charge policy, optimization of processes and methods is still facing many difficulties. In this paper, the model parameters and toll status of various goods vehicles are considered, and an optimization algorithm of toll rates for different vehicles in a large-scale road network is proposed. By constructing a traffic demand prediction model based on multiple truck classification, this paper analyzes the distribution status of network trucks and the final charging under the influence of different rates. At the bottom of the algorithm is an analytical model composed of nonlinear equations whose dimensions scale linearly with the scale of the road network. The scale of the road network is independent of the path set and link attribute. The model is verified and the parameters are calibrated by a small network. Finally, the Road network is selected for empirical analysis in Xinjiang Autonomous Region. A case study shows that the analytical structure information provided by the analytic network model enables the algorithm to quickly identify high quality solutions, and the algorithm has better simulation accuracy and premium rate design advantages.

Traditional route planning problems mainly focus on finding the shortest path considering the travel distance or time. In this paper, we aim to find the most scenic path that offers the most beautiful sceneries on the arcs of a path while the total travel cost (distance or time) is within a user-specified budget. This is a challenging problem as the optimization objective is to maximize the value of the path (i.e., its scenic value) instead of minimizing its cost (distance or time). The problem can be formulated as a variant of the Arc Orienteering Problem (AOP), which is a well-known NP-hard combinatorial optimization problem. Due to the fast response-time requirements of interactive mobile and online applications (e.g., within 300 milliseconds) and the large scale of real-world road networks, existing heuristic algorithms for AOP fail to solve the most scenic road problem. Therefore, unlike the existing approaches for AOP where they treat the road network as a traditional graph in which all-pair distances are pre-computed a priori, in this work, we treat the road network as a spatial network, utilizing the techniques from the field of spatial database: ellipse pruning and spatial indexing. Experiments on two real-world datasets demonstrate the efficiency and accuracy of our proposed algorithms, which can achieve over 95% accuracy within 300 milliseconds on large-scale datasets (over 100K network nodes).

Co-evolutionary traffic signal control using reinforcement learning for road networks under stochastic capacity

A theorem on the expected complexity of dijkstra's shortest path algorithm

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.

Mobile users prefer to choose personalized travel routes using their mobile terminals. Keyword-aware Optimal Route Query (KORQ) is proposed to meet users' need because it not only considering the length of the route, but also considering the cost of the route and the points of interest covered by the route. As the number of points of interest in road networks increases sharply, the time and space complexity for preprocessing and route expansion rises dramatically, and the state of the art algorithms are not scalable. To address these issues, we propose an algorithm called KORAL, short for Keyword-aware Optimal Route Query Algorithm on Large-scale Road Networks. To reduce the overhead of preprocessing, KORAL partitions the road network into subgraphs, and stores only the information about the routes between subgraphs in preprocessing stages. In the rout expansion stage, KORAL uses a strategy called minimum budget pruning to prune infeasible vertices, which greatly speed up the route expansion. Experiments against 3 datasets of New York road network in a server with 16G RAM show that KORAL is scalable and breaks the limitation that the road network cannot exceed 100K vertices.

Geographic information systems related to the position of objects in the earth's surface such as the position of the attractions that are connected with roads. Streets that are interconnected to form a complex network. Usually people use our manual to find the shortest route of an object toward a particular object but it is less than optimal because it requires precision and a long time. The shortest route search problem has been solved by several algorithms such as Dijkstra's algorithm, Astar, Floyd Warshall, Ant Colony and others. Based on this final task is to discuss the implementation of the shortest route to the geographic information system of tourism in a city using the distance parameter. City to be addressed is Sawahlunto has 12 attractions that are connected with road network. Shortest path search algorithm used is Dijkstra's and Astar algorithm. Geographic information system of tourism is displayed in a web form, with the programming language PHP, database PosgreSQL and support PostGIS and pgRouting. Based on the testing of these applications can provide the shortest route along the travel distance to and from 12 tourist sites in Sawahlunto. Astar algorithm is faster in the process of finding the shortest route instead of Dijkstra's algorithm with an average gap of 40 ms. Application also provides information supporting the tourism profile information, attractions, culture, and contacts. Keyword : shortest path, Dijkstra algorithm, Astar algorithm, geographic information system

Shortest path problem with uncertain arc lengths

The single-source shortest paths problem (SSSP) is one of the classic problems in algorithmic graph theory: given a positively weighted graph G with a source vertex s , find the shortest path from s to all other vertices in the graph. Since 1959, all theoretical developments in SSSP for general directed and undirected graphs have been based on Dijkstra's algorithm, visiting the vertices in order of increasing distance from s . Thus, any implementation of Dijkstra's algorithm sorts the vertices according to their distances from s . However, we do not know how to sort in linear time. Here, a deterministic linear time and linear space algorithm is presented for the undirected single source shortest paths problem with positive integer weights. The algorithm avoids the sorting bottleneck by building a hierarchical bucketing structure, identifying vertex pairs that may be visited in any order.

The shortest path problem (SPP) constitutes one of the most frequently encountered classes of problems in graph theory. It is certainly the most fundamental of components in the fields of transportation and communication networks. Shortest path problems may be encountered directly, possibly as a result of a clever formulation of a problem not at first sight involving shortest paths, or indirectly as a subproblem in the solution of a more complicated optimization problem. This use of shortest path problems as subroutines motivates the search for algorithms with good theoretical bounds on running time. We also seek computer implementations whose empirical performances are rapid in spite of perhaps weak theoretical bounds for the algorithms they implement. As testimony to the importance of shortest path and related problems, a large number of surveys, annotated bibliographies, and reviews have appeared over the past thirty years. Among them are those by Dreyfus (1969), Pierce (1975), Golden and Magnanti (1977), and Gallo and Pallottino (1988).

Hybrid deep learning models for traffic prediction in large-scale road networks