Finding shortest paths on real road networks: the case for A*

Labeling methods for partially ordered paths

The order k Voronoi diagram (OkVD) is an effective geometric construction to partition the geographical space into a set of Voronoi regions such that all locations within a Voronoi region share the same k nearest points of interest (POIs). Despite the broad applications of OkVD in various geographical analysis, few efficient algorithms have been proposed to construct OkVD in real road networks. This study proposes a novel algorithm consisting of two stages. In the first stage, a new one-to-all k shortest path finding procedure is proposed to efficiently determine the shortest paths to k nearest POIs for each node. In the second stage, a new recursive procedure is introduced to effectively divide boundary links within different Voronoi regions using the hierarchical tessellation property of the OkVD. To demonstrate the applicability of the proposed OkVD construction algorithm, a case study of place-based accessibility evaluation is carried out. Computational experiments are also conducted on five real road networks with different sizes, and results show that the proposed OkVD algorithm performed significantly better than state-of-the-art algorithms.

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.

This article analyzes problems of determining the shortest path and optimal route amongst the given stoppages. The model of the problem is presented as a directional graph, where nodes are pickup points (termed as stoppage point in database) and crossings outside stoppage points and edges are roads among stoppage points and crossings. Each node has some information attached to it: stoppageId, stoppageName, latitude, longitude and numberOfPassengers of the stop, maintenance organizations, and mark(s) of the crossing(s). All pickup points are connected by roads. These roads are considered as the edges of the graph. Edges also have information attached to it: roadId, source, destination, distance, time etc.We have selected Floyd Warshall algorithm to nd the shortest path between two stoppages. This algorithm works in two stages: in rst stage, it nds the shortest path between all stoppages, and in second stage it nds optimized route to visit some of these stoppages. The solution is displayed in the form of shortest distance and time between two locations. The program is written in java language. It uses 3 tables as input from database : nodes, vehicle details and road. This paper gives implementation outcome of Floyd Warshall algorithm to solve the all pairs shortestpath problem for directed road graph system. We have considered an example of a map of Pune. Keyword: Adjacency matrix,intermediate path,optimal route, shortest path,transitive closure I. Introduction Now days in the current scenario companies and schools provide transportation facilities to their employees and students from their organizations to their respective houses and vice versa. The purpose of this article is to present an interface between a traveling agency and its traveller so that, the subscribers can keep a track of the service they have subscribed.A key problem in public conveyance system is the computation of shortest paths between di erent locations for a given region. Sometimes this computation has to be done in real time. During the literature survey we found how di cult it is to nd the shortest path covering all pickup points and how to allocate available transport vehicles to these speci c routes manually. There is always a need to nd optimal path for their operational viability. So, just the idea that our system will help in e cient allocation of vehicles and shortest route creation to save time and fuel consumption. The system scope is to design such system for a small area of the city.

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

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.

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).

Solving the shortest path problem is important in achieving high performance or to efficiently utilize resources in various kinds of networks, e.g., data communication networks and transportation networks. Fortunately, under independent additive link weights, this problem is solvable in polynomial time. However, in many real-life networks, the link weights (e.g., delay, bandwidth, failure probability) are often correlated due to spatial or temporal dependencies. These correlated link weights together might behave in a different manner and are not always additive. In this paper, we first propose two correlated link-weight models, namely (i) the deterministic correlated model and (ii) the (log-concave) stochastic correlated model. Subsequently, we study the shortest path problem under these two correlated models. We prove that the shortest path problem is NP-hard under the deterministic correlated model, and even cannot be approximated to arbitrary degree in polynomial time. On the other hand, we show that the shortest path problem is polynomial-time solvable under a nodal deterministic correlated model. Finally, we show that the shortest path problem under the (log-concave) stochastic correlated model can be solved by convex optimization.

Parametric search for the bi-attribute concave shortest path problem

Keyword index volumes 72–79 (1994)

Shortest path problem with uncertain arc lengths

Finding the minimum cost in the shortest path (SP) problem is one of the most important and fundamental problems in network applications. In the current chapter due to the uncertainty caused by the data that occurs in the real world, we use various tools in the fuzzy set theory to perform the cost of arc lengths. First, assume that the arcs are in the form of interval fuzzy sets. Using the well-known max-min criterion provided by Bellman and Zadeh for fuzzy decision making, model formulation is performed as a problem of nonlinear and mixed number programming. then describe the algorithm based on reliability, thereafter another method based on interval-valued calculation and Dijkstra’s algorithm mentioned. at the end with example, we analyze the performance of the methods and compare the results. Then we introduce the (SP) problem in hesitant fuzzy environment and develop the two mentioned methods to solve hesitant fuzzy shortest path (HFSP) problem. Numerical example shows the efficiency of developed methods. Then we show the length of the arcs with hesitant fuzzy sets. In this case, we solve the fuzzy shortest path problem by introducing a new distance function and ranking. Numerical results are obtained using LINGO and MATLAB software.

On scenario construction for stochastic shortest path problems in real road networks

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.