Routing In Road Networks Research Articles

Robust Routing Using Electrical Flows

Generating alternative routes in road networks is an application of significant interest for online navigation systems. A high quality set of diverse alternate routes offers two functionalities - (a) support multiple (unknown) preferences that the user may have; and (b) robust changes in network conditions. We formulate a new quantification of the latter in this paper, and propose a novel method to produce alternative routes based on concepts from electrical flows and their decompositions. Our method is fundamentally different from the main techniques that produce alternative routes in road networks, which are the penalty and the plateau methods, with the former providing high quality results but being too slow for practical use and the latter being fast but suffering in terms of quality. We evaluate our method against the penalty and plateau methods, showing that it is as fast as the plateau method while also recovering much of the headroom towards the quality of the penalty method. The metrics we use to evaluate performance include the stretch (the average cost of the routes), the diversity , and the robustness (the connectivity between the origin and destination) of the induced set of routes.

Using Incremental Many-to-One Queries to Build a Fast and Tight Heuristic for A* in Road Networks

We study exact, efficient, and practical algorithms for route planning applications in large road networks. On the one hand, such algorithms should be able to answer shortest path queries within milliseconds. On the other hand, routing applications often require integrating the current traffic situation, planning ahead with predictions for future traffic, respecting forbidden turns, and many other features depending on the specific application. Therefore, such algorithms must be flexible and able to support a variety of problem variants. In this work, we revisit the A* algorithm to build a simple, extensible, and unified algorithmic framework applicable to many route planning problems. A* has been previously used for routing in road networks. However, its performance was not competitive because no sufficiently fast and tight distance estimation function was available. We present a novel, efficient, and accurate A* heuristic using Contraction Hierarchies, another popular speedup technique. The core of our heuristic is a new Contraction Hierarchies query algorithm called Lazy RPHAST , which can efficiently compute shortest distances from many incrementally provided sources toward a common target. Additionally, we describe A* optimizations to accelerate the processing of low-degree vertices, which are typical in road networks, and present a new pruning criterion for symmetrical bidirectional A*. An extensive experimental study confirms the practicality of our approach for many applications.

Candidate Sets for Alternative Routes in Road Networks (Extended Abstract)

We present a fast algorithm with preprocessing for computing multiple good alternative routes in road networks. Our approach is based on single via node routing on top of Contraction Hierarchies and achieves superior quality and efficiency compared to previous methods. The algorithm has neglectable memory overhead.

On matchings, T‐joins, and arc routing in road networks

AbstractMatchings and T‐joins are fundamental and much‐studied concepts in graph theory and combinatorial optimization. One important application of matchings and T‐joins is in the computation of strong lower bounds for arc routing problems (ARPs). An ARP is a special kind of vehicle routing problem, in which the demands are located along edges or arcs, rather than at nodes. We point out that the literature on applying matchings and T‐joins to ARPs does not fully exploit the structure of real‐life road networks. We propose some ways to exploit this structure. Computational results show significant running time improvements, without deteriorating the quality of the lower bounds.

Enhanced Indexing and Querying of Trajectories in Road Networks via String Algorithms

In this article, we propose a novel indexing and querying method for trajectories constrained in a road network. We aim to provide efficient algorithms for various types of spatiotemporal queries that involve routing in road networks, such as (1) finding moving objects that have traveled along a given path during a given time interval, (2) extracting all paths traveled after a given spatiotemporal context, and (3) enumerating all paths between two locations traveled during a certain time interval. Unlike the existing methods in spatial database research, we employ indexing techniques and algorithms from string processing. This idea is based on the fact that we can represent spatial paths as strings, because trajectories in a network are represented as sequences of road segment IDs. The proposed SNT-index (<u>s</u>uffix-array-based <u>n</u>etwork-constrained <u>t</u>rajectory index) introduces two novel concepts to trajectory indexing. The first is FM-index, which is a compact in-memory data structure for pattern matching. The second is an inverse suffix array, which allows the FM-index to be integrated with the temporal information stored in a forest of B + -trees. Thanks to these concepts, we can reduce the number of B + -tree accesses required by the query processing algorithms to a constant number, something that cannot be achieved with existing methods. Although an FM-index is essentially a static index, we also propose a practical method of appending new data to the index. Finally, experiments show that our method can process the target queries for more than 1 million trajectories in a few tens of milliseconds, which is significantly faster than what the baseline algorithms can achieve without string algorithms.

Candidate Sets for Alternative Routes in Road Networks

We study the computation of good alternatives to the shortest path in road networks. Our approach is based on single via-node routing on top of contraction hierarchies and achieves superior quality and efficiency compared to previous methods. We present a fast preprocessing method for computing multiple good alternatives and apply this result in an online setting. This setting makes our result applicable in legacy systems with negligible memory overhead. An extensive experimental analysis on a continental-sized real- world road network proves the performance of our algorithm and supports the general systematic algorithm engineering approach. We also show how to combine our results with the competing concept of alternative graphs that encode many alternative paths at once.

Alternative routes in road networks

We study the problem of finding good alternative routes in road networks. We look for routes that are substantially different from the shortest path, have small stretch, and are locally optimal. We formally define the problem of finding alternative routes with a single via vertex, develop efficient algorithms for it, and evaluate them experimentally. Our algorithms are efficient enough for practical use and compare favorably with previous methods in both speed and solution quality.

Exact Routing in Large Road Networks Using Contraction Hierarchies

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.

Applications of graph algorithms in GIS

This paper describes ongoing PhD research on applications of graph algorithms in Geographical Information Systems. Many GIS problems can be translated into a graph problem, especially in the domain of routing in road networks. Our research aims to evaluate and develop efficient methods for different variants of the routing problem. Standard existing shortest path algorithms are not always suited for use in road networks, e.g. in a realistic situation forbidden turns and turn penalties need to be taken into account. An experimental evaluation of different methods for this purpose is presented. Another interesting problem is the generation of alternative routes. This can be modelled as a k shortest paths problem, where a ranking of k paths is desired rather than only the shortest path itself. A new heuristic approach for generating alternative routes is presented and evaluated.

Fast Routing in Road Networks with Transit Nodes

When you drive to somewhere far away, you will leave your current location via one of only a few important traffic junctions. Starting from this informal observation, we developed an algorithmic approach, transit node routing, that allows us to reduce quickest path queries in road networks to a small number of table lookups. For road maps of Western Europe and the United States, our best query times improved over the best previously published figures by two orders of magnitude. This is also more than one million times faster than the best known algorithm for general networks.