Extracting Small Subgraphs in Road Networks

Highway hierarchies exploit hierarchical properties inherent in real-world road networks to allow fast and exact point-to-point shortest-path queries. A fast preprocessing routine iteratively performs two steps: First, it removes edges that only appear on shortest paths close to source or target; second, it identifies low-degree nodes and bypasses them by introducing shortcut edges. The resulting hierarchy of highway networks is then used in a Dijkstra-like bidirectional query algorithm to considerably reduce the search space size without losing exactness. The crucial fact is that ‘far away’ from source and target it is sufficient to consider only high-level edges. Experiments with road networks for a continent show that using a preprocessing time of around 15 min, one can achieve a query time of around 1ms on a 2.0GHz AMD Opteron. Highway hierarchies can be combined with goal-directed search, they can be extended to answer many-to-many queries, and they can be used as a basis for other speed-up techniques (e.g., for transit-node routing and highway-node routing).

Contraction hierarchies are a simple approach for fast routing in road networks. Our algorithm calculates exact shortest paths and handles road networks of whole continents. During a preprocessing step, we exploit the inherent hierarchical structure of road networks by adding shortcut edges. A subsequent modified bidirectional Dijkstra algorithm can then find a shortest path in a fraction of a millisecond, visiting only a few hundred nodes. This small search space makes it suitable to implement it on a mobile device. We present a mobile implementation that also handles changes in the road network, like traffic jams, and that allows instantaneous routing without noticeable delay for the user. Also, an algorithm to calculate large distance tables is currently the fastest if based on contraction hierarchies.

We present a new way of analyzing Contraction Hierarchies (CH), a widely used speed-up technique for shortest path computations in road networks. In previous work, preprocessing and query times of deterministically constructed CH on road networks with n nodes were shown to be polynomial in n as well as the highway dimension h of the network and its diameter D. While h is conjectured to be polylogarithmic for road networks, a tight bound remains an open problem. We rely on the empirically justifiable assumption of the road network exhibiting small growth. We introduce a method to construct randomized Contraction Hierarchies on road networks as well as a probabilistic query routine. Our analysis reveals that randomized CH lead to sublinear search space sizes in the order of $$\sqrt{n} \log \sqrt{n}$$ , auxiliary data in the order of $$n \log ^2 \sqrt{n}$$ , and correct query results with high probability after a polynomial time preprocessing phase.

Computing top-k nearest neighbors (kNN) is a fundamental problem in road networks. Existing solutions either need a complicated parameter configuration in index construction or incur high costs when scanning an unbounded number of vertices in query processing. In this paper, we propose a novel parameter-free index-based solution for the kNN query based on the concept of tree decomposition in large road networks. Based on our index structure, we propose an efficient and progressive algorithm that returns each result in a bounded delay. We also optimize the index structure, which improves the efficiency of both index construction and index maintenance in large road networks. We conduct extensive experiments to show the efficiency of our proposed algorithms and the effectiveness of our optimization techniques in real-world road networks from ten regions.

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.

We propose a simple and effective heuristic that allows fast generation of a large set of shortest path alternatives in weighted directed graphs. The heuristic is based on existing deviation path algorithms for exact k shortest paths. It precalculates a backward shortest path tree and thus avoids doing many shortest path computations, but as a result it does not necessarily find the exact set of k shortest paths. Computational results on real-world road networks are reported. Our tests show that the quality of the paths produced by the heuristic is most satisfactory: typically, the kth path found by the heuristic is less than 1% longer than the exact kth shortest path, for values of k up to 10,000. Moreover, the heuristic runs very fast. We also show how the heuristic can be enhanced to an exact k shortest paths algorithm, which performs well in comparison with the existing exact k shortest path algorithms.

Real-time scheduling and routing of shared autonomous vehicles considering platooning in intermittent segregated lanes and priority at intersections in urban corridors

In this paper, the Periodic Capacitated Arc Routing Problem (PCARP) is investigated. PCARP is an extension of the well-known CARP from a single period to a multi-period horizon. In PCARP, two objectives are to be minimized. One is the number of required vehicles (nv), and the other is the total cost (tc). Due to the multi-period nature, given the same graph or road network, PCARP can have a much larger solution space than the single-period CARP counterpart. Furthermore, PCARP consists of an additional allocation sub-problem (of the days to serve the arcs), which is interdependent with the routing sub-problem. Although some attempts have been made for solving PCARP, more investigations are yet to be done to further improve their performance especially on large-scale problem instances. It has been shown that optimizing nv and tc separately (hierarchically) is a good way of dealing with the two objectives. In this paper, we further improve this strategy and propose a new Route Decomposition (RD) operator thereby. Then, the RD operator is integrated into a Memetic Algorithm (MA) framework for PCARP, in which novel crossover and local search operators are designed accordingly. In addition, to improve the search efficiency, a hybridized initialization is employed to generate an initial population consisting of both heuristic and random individuals. The MA with RD (MARD) was evaluated and compared with the state-of-the-art approaches on two benchmark sets of PCARP instances and a large data set which is based on a real-world road network. The experimental results suggest that MARD outperforms the compared state-of-the-art algorithms, and improves most of the best-known solutions. The advantage of MARD becomes more obvious when the problem size increases. Thus, MARD is particularly effective in solving large-scale PCARP instances. Moreover, the efficacy of the proposed RD operator in MARD has been empirically verified. Graphical abstract https://ars.els-cdn.com/content/image/1-s2.0-S1568494616304768-fx1_lrg.jpg © This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/

The mixed truck-drone delivery system has attracted increasing attention for its potential to optimize last-mile logistics. While the Flying Sidekick Traveling Salesman Problem (FSTSP) provides a foundation for modeling the truck-drone collaboration, it falls short of capturing real-world complexities by assuming a single truck-drone pair operating on a fully connected graph. We introduce the Multi-Agent FSTSP (MA-FSTSP), which extends FSTSP to handle multiple trucks, each carrying multiple drones operating over real road networks. Trucks must follow roads, while drones can fly directly between locations. To solve this NP-hard problem efficiently, we propose a novel three-phase algorithm that first partitions customers using a set-based distance heuristic, then computes initial truck routes via a Set TSP formulation, and finally optimizes drone deployment patterns by dynamic programming. Through extensive experiments on real-world road networks from Manhattan (1,024 nodes) and Boston (11,000 nodes), we demonstrate that our method achieves more than 30% cost reduction compared to existing approaches while scaling effectively to problems with 150 customers within a 20-minute computational time-bound.

To study the relationship of different reliability indices for road network under stochastic demand, an evaluation method based on travel time reliability (TTR) was set up for level of service (Los) reliability. Assuming that travelers acquire the variation of the route travel time based on past experiences and factor such variability into their route choice considerations in the form of travel time budget, which was defined as the minimal travel time that can accommodate a specified travel time reliability and can be derived according to the probability characteristics of log-normal distribution. Accordingly, Los reliability evaluation models of link and road network were proposed based on the link flow distribution, which can be determined by a travel time budget-based variational inequality (VI) network equilibrium model and a route-based solution algorithm. Some numerical studies on a small road network were presented to validate the proposed method and algorithm.

The paper considers an approach to the construction of fuzzy structured numerical sets based on the formation of a fuzzy original of a special type with subsequent replication on the number axis. The constructive principle of fuzzy original formalization is to define a fuzzy triangular number with the appropriate support. A variant of the formation of fuzzy numerical sets, formalizing the "fast" and "slow" passage of time, is proposed. The developed technique allows us to propose a solution to the problem associated with the formalization of the subjective perception of the time reference in processes involving a person, to obtain results and evaluate the impact of fuzzy description and taking into account the dynamics of the time reference on the solution of various optimization problems. A general approach to the formation and solution of fuzzy linear optimization problems is considered, the transition from fuzzy to parametric formulation in the Bellman-Zade form is described. Examples of the use of fuzzy flow of time for different statements of tasks that arise when determining the order of the set of tasks within a given time interval with or without additional restrictions on the execution process are considered. An approach is proposed for the correction of the initial time distribution plans, taking into account different rates of time counting. A mathematical model of the fuzzy traveling salesman problem is formulated as a problem of finding a route to visit a given number of cities without repetitions with a minimum travel time with time parameters specified as right fuzzy numbers, the support value in which depends on various external conditions and factors. The results of calculations of solutions of fuzzy optimization problems are obtained. The influence of the speed of the passage of time on the solution of the considered optimization problems is determined.

We propose a conceptual framework to be utilized by developers of applications that require alternative routes in road networks. Our framework implements an efficient approach for dynamic alternative route planning that can respond to road network changes. With our framework, state-of-the-art algorithms for alternative route planning can be enabled to cope better with dynamic changes. We design a conceptual graph data model to reflect the semantic context of alternative route planning, and propose a dynamic index to store and reuse alternative routes. Our experiments with real-world road network data indicate that our framework can generate high-quality alternative routes in dynamic road networks efficiently. KeywordsGeographic informationData modellingGraph database

Information-based demand measures using social routing advice are receiving increasing attention, as they are expected to be successful in reducing the traffic congestion. Such measures direct travelers toward routes that benefit the road network. As such, some travelers need to act socially and take a detour. This paper explores the impacts on network performance and equity that result from the application of a social routing service. We complement the existing work by using a large-scale real-world road network, by assessing impacts on the individual level and by discussing our findings in the light of observed individual compliance behavior obtained from a field experiment. Our results show that 3.6% of total travel time within our road network could be reduced when all trips are made in compliance with the received advice. However, based on the observed compliance behavior, a social routing service is expected to direct only a minority of travelers toward social routes. We show how the attained travel time savings vary with the assumed compliance rate, e.g., to achieve 50% of the potential travel time savings, about 30% of travelers need to be willing to take a detour. Moreover, we find that lower the compliance among travelers, the more the social travelers need to compensate for the selfish behavior of others by taking longer detours. Finally, we demonstrate that the impacts on network performance and equity highly depend on the spatial distribution of social travelers among origins and destinations.

A vehicle in road networks shares location data with other vehicles and location-based services (LBS) through Internet-of-vehicles (IoV). By analyzing the location data from vehicles, LBS providers can offer vehicles better services. However, fake trajectories created by adversaries and malicious drivers diminish the location data utility in IoV and breach the quality of LBS. Illegal trajectory detection is vital to ensure location data utility in IoV. Existing location privacy-preserving schemes like obfuscation schemes add noise to actual location data increasing difficulties in detecting illegal trajectories. In this paper, we detect illegal trajectory in the case that all drivers in road networks protect location privacy by using obfuscation. We propose a new personalized obfuscation mechanism to dynamically and adaptively protect the location privacy of drivers in road networks. Considering uneven protection, we propose a trajectory detection scheme to classify trajectories in IoV. We evaluate our detection method with the data of real-world road networks, which is an important scenario of smart cities. The experiment results show that the proposed classifier outperforms existing studies in detecting malicious obfuscated trajectories with at least 94% of the Area Under the Curve (AUC) score.

The current widespread use of location-based services and GPS technologies has revived interest in very fast and scalable shortest path queries. We introduce a new shortest path query type in which dynamic constraints may be placed on the allowable set of edges that can appear on a valid shortest path (e.g., dynamically restricting the type of roads or modes of travel which may be considered in a multimodal transportation network). We formalize this problem as a specific variant of formal language constrained shortest path problems, which we call the Kleene Language Constrained Shortest Paths problem. To efficiently support this type of dynamically constrained shortest path query for large-scale datasets, we extend the hierarchical graph indexing technique known as Contraction Hierarchies. Our experimental evaluation using the North American road network dataset (with over 50 million edges) shows an average query speed and search space improvement of over 3 orders of magnitude compared to the naïve adaptation of the standard Dijkstra's algorithm to support this query type. We also show an improvement of over 2 orders of magnitude compared to the only previously-existing indexing technique which could solve this problem without additional preprocessing.