The current paper deals with the subject of shortest path routing in transportation networks (in terms of travelling time), where the speed in several of the network's roads is a function of the time interval. The main contribution of the paper is a procedure that is faster compared to the conventional approaches, that derives the road's traversal time according to the time instant of departure, for the case where the road's speed has a constant value inside each time interval (in general, different value for each time interval). Furthermore, the case where the road's speed is a linear function of time inside each time interval (in general, different linear function for each time interval) is investigated. A procedure that derives the road's traversal time according to the time instant of departure is proposed for this case as well. The proposed procedures are combined with Dijkstra's algorithm and the resulting algorithms, that are practically applicable and of low complexity, provide optimal shortest path routing in the networks under investigation.
Dynamic graph research is an essential subject in Computer Science. The shortest path problem is still the central in this field; moreover there is a variety of applications in practical projects. In this paper, we select the transportation activity as a paradigm to study. Of course there exists the most clear and appealing practical application over the intelligent navigation, also which is an important part in intelligent transportation system (ITS). Totally speaking, this activity is fairly simple and well-behavior under our consideration, for which, there is a lot of sophisticated theories…
The design of efficient transportation networks is an important challenge in many research areas. Among the most promising recent methods, biological routing mimic local rules found in nature. However comparisons with other methods are rare. In this paper we define a common framework to compare network design method. We use it to compare biological and a shortest-path routing approaches. We find that biological routing explore a more efficient set of solution when looking to design a network for uniformly distributed transfers. However, the difference between the two approaches is not as impor…
Shortest path queries over graphs are usually considered as isolated tasks, where the goal is to return the shortest path for each individual query. In practice, however, such queries are typically part of a system (e.g., a road network) and their execution dynamically affects other queries and network parameters, such as the loads on edges, which in turn affects the shortest paths. We study the problem of collectively processing shortest path queries, where the objective is to optimize a collective objective, such as minimizing the overall cost. We define a temporal load-aware network that dy…
The problem of identifying the k-shortest paths (KSPs for short) in a dynamic road network is essential to many location-based services. Road networks are dynamic in the sense that the weights of the edges in the corresponding graph constantly change over time, representing evolving traffic conditions. Very often such services have to process numerous KSP queries over large road networks at the same time, thus there is a pressing need to identify distributed solutions for this problem. However, most existing approaches are designed to identify KSPs on a static graph in a sequential manner (i.e…
We study the earliest arrival problem in road networks with static time-dependent functions as arc weights. We propose and evaluate the following simple algorithm: (1) average the travel time in k time windows, (2) compute a shortest time-independent path within each window and mark the edges in these paths, and (3) compute a shortest time-dependent path in the original graph restricted to the marked edges. Our experimental evaluation shows that this simple algorithm yields near optimal results on well-established benchmark instances. We additionally demonstrate that the error can be further r…
Finding the shortest path between two points in a graph is a fundamental problem that has been well-studied over the past several decades. Shortest path algorithms are commonly applied to modern navigation systems, so our study aims to improve the efficiency of an existing algorithm on large-scale Euclidean networks. The current literature lacks a deep understanding of certain algorithms' performance on these types of networks. Therefore, we incorporate a new heuristic function, called the $k$-step look-ahead, into the A* search algorithm and conduct a computational experiment to evaluate and …
We present algorithms for multi-modal route planning in road and public transit networks, as well as in combined networks. Therefore, we explore the nearest neighbor and shortest path problem and propose solutions based on Cover-Trees, ALT and CSA. Further, we illustrate the theory behind the algorithms, give a short overview of other techniques, present experimental results and compare the techniques with each other.
In this paper, we re-evaluate the basic strategies for label correcting algorithms for the multiobjective shortest path (MOSP) problem, i.e., node and label selection. In contrast to common believe, we show that---when carefully implemented---the node-selection strategy usually beats the label-selection strategy. Moreover, we present a new pruning method which is easy to implement and performs very well on real-world road networks. In this study, we test our hypotheses on artificial MOSP instances from the literature with up to 15 objectives and real-world road networks with up to almost 160,0…
We study the problem of quickly computing point-to-point shortest paths in massive road networks with traffic predictions. Incorporating traffic predictions into routing allows, for example, to avoid commuter traffic congestions. Existing techniques follow a two-phase approach: In a preprocessing step, an index is built. The index depends on the road network and the traffic patterns but not on the path start and end. The latter are the input of the query phase, in which shortest paths are computed. All existing techniques have large index size, slow query running times or may compute suboptima…
In the era of the proliferation of Geo-Spatial Data, induced by the diffusion of GPS devices, the map matching problem still represents an important and valuable challenge. The process of associating a segment of the underlying road network to a GPS point gives us the chance to enrich raw data with the semantic layer provided by the roadmap, with all contextual information associated to it, e.g. the presence of speed limits, attraction points, changes in elevation, etc. Most state-of-art solutions for this classical problem simply look for the shortest or fastest path connecting any pair of co…
We study the problem of minimizing overall trip time for battery electric vehicles in road networks. As battery capacity is limited, stops at charging stations may be inevitable. Careful route planning is crucial, since charging stations are scarce and recharging is time-consuming. We extend the Constrained Shortest Path problem for electric vehicles with realistic models of charging stops, including varying charging power and battery swapping stations. While the resulting problem is NP-hard, we propose a combination of algorithmic techniques to achieve good performance in practice. Extensive …
We present an algorithm for the k shortest simple path problem on weighted directed graphs (kSSP) that is based on Eppstein's algorithm for a similar problem in which paths are allowed to contain cycles. In contrast to most other algorithms for kSSP, ours is not based on Yen's algorithm and does not solve replacement path problems. Its worst-case running time is on par with state-of-the-art algorithms for kSSP. Using our algorithm, one may find O(m) simple paths with a single shortest path tree computation and O(n + m) additional time per path in well-behaved cases, where n is the number of no…
The increase in the world's population and rising standards of living is leading to an ever-increasing number of vehicles on the roads, and with it ever-increasing difficulties in traffic management. This traffic management in transport networks can be clearly optimized by using information and communication technologies referred as Intelligent Transport Systems (ITS). This management problem is usually reformulated as finding the shortest path in a time varying random graph. In this article, an online shortest path computation using stochastic gradient descent is proposed. This routing algori…
National University of Singapore（新加坡国立大学）；École polytechnique fédérale de Lausanne（洛桑联邦理工学院）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）；Ariel University（阿里埃勒大学）
Reconfiguring two shortest paths in a graph means modifying one shortest path to the other by changing one vertex at a time so that all the intermediate paths are also shortest paths. This problem has several natural applications, namely: (a) revamping road networks, (b) rerouting data packets in synchronous multiprocessing setting, (c) the shipping container stowage problem, and (d) the train marshalling problem. When modelled as graph problems, (a) is the most general case while (b), (c) and (d) are restrictions to different graph classes. We show that (a) is intractable, even for relaxed va…
