We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.

/pdf/route-planning-in-transportation-networks-k0typz8i4k.pdf

Route Planning in Transportation Networks

We survey research on self-driving cars published in the literature focusing on autonomous cars developed since the DARPA challenges, which are equipped with an autonomy system that can be categorized as SAE level 3 or higher. The architecture of the autonomy system of self-driving cars is typically organized into the perception system and the decision-making system. The perception system is generally divided into many subsystems responsible for tasks such as self-driving-car localization, static obstacles mapping, moving obstacles detection and tracking, road mapping, traffic signalization detection and recognition, among others. The decision-making system is commonly partitioned as well into many subsystems responsible for tasks such as route planning, path planning, behavior selection, motion planning, and control. In this survey, we present the typical architecture of the autonomy system of self-driving cars. We also review research on relevant methods for perception and decision making. Furthermore, we present a detailed description of the architecture of the autonomy system of the self-driving car developed at the Universidade Federal do Espirito Santo (UFES), named Intelligent Autonomous Robotics Automobile (IARA). Finally, we list prominent self-driving car research platforms developed by academia and technology companies, and reported in the media.

Self-driving cars: A survey

Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to three million times faster than Dijkstra's algorithm. We give an overview of the techniques enabling this development and point out frontiers of ongoing research on more challenging variants of the problem that include dynamically changing networks, time-dependent routing, and flexible objective functions.

/pdf/engineering-route-planning-algorithms-4j73fozavy.pdf

Engineering Route Planning Algorithms

We study the point-to-point shortest path problem in a setting where preprocessing is allowed. We improve the reach-based approach of Gutman [17] in several ways. In particular, we introduce a bidirectional version of the algorithm that uses implicit lower bounds and we add shortcut arcs to reduce vertex reaches. Our modifications greatly improve both preprocessing and query times. The resulting algorithm is as fast as the best previous method, due to Sanders and Schultes [28]. However, our algorithm is simpler and combines in a natural way with A* search, which yields significantly better query times.

/pdf/reach-for-a-efficient-point-to-point-shortest-path-qwd54wmnxs.pdf

Reach for A : efficient point-to-point shortest path algorithms

Abraham et al. [SODA 2010] have recently presented a theoretical analysis of several practical point-to-point shortest path algorithms based on modeling road networks as graphs with low highway dimension. They also analyze a labeling algorithm. While no practical implementation of this algorithm existed, it has the best time bounds. This paper describes an implementation of the labeling algorithm that is faster than any existing method on continental road networks.

/pdf/a-hub-based-labeling-algorithm-for-shortest-paths-in-road-2xtonimcev.pdf

A hub-based labeling algorithm for shortest paths in road networks

An overlay graph of a given graph G = (V, E) on a subset S ⊆ V is a graph with vertex set S and edges corresponding to shortest paths in G. In particular, we consider variations of the multilevel overlay graph used in Schulz et al. [2002] to speed up shortest-path computation. In this work, we follow up and present several vertex selection criteria, along with two general strategies of applying these criteria, to determine a subset S of a graph's vertices. The main contribution is a systematic experimental study where we investigate the impact of selection criteria and strategies on multilevel overlay graphs and the resulting speed-up achieved for shortest-path computation: Depending on selection strategy and graph type, a centrality index criterion, selection based on planar separators, and vertex degree turned out to perform best.

https://epubs.siam.org/doi/pdf/10.1137/1.9781611972863.15

Engineering multilevel overlay graphs for shortest-path queries

In practice, computing a shortest path from one node to another in a directed graph is a very common task. This problem is classically solved by Dijkstra's algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality of the solution can still be guaranteed. In most studies, such techniques are considered individually. The focus of our work is combination of speed-up techniques for Dijkstra's algorithm. We consider all possible combinations of four known techniques, namely, goal-directed search, bidirectional search, multilevel approach, and shortest-path containers, and show how these can be implemented. In an extensive experimental study, we compare the performance of the various combinations and analyze how the techniques harmonize when jointly applied. Several real-world graphs from road maps and public transport and three types of generated random graphs are taken into account.

Combining speed-up techniques for shortest-path computations

An overlay graph of a given graph G = (V, E) on a subset S ⊆ V is a graph with vertex set S that preserves some property of G. In particular, we consider variations of the multi-level overlay graph used in [21] to speed up shortest-path computations. In this work, we follow up and present general vertex selection criteria and strategies of applying these criteria to determine a subset S inducing an overlay graph. The main contribution is a systematic experimental study where we investigate the impact of selection criteria and strategies on multi-level overlay graphs and the resulting speed-up achieved for shortest-path queries. Depending on selection strategy and graph type, a centrality index criterion, a criterion based on planar separators, and vertex degree turned out to be good selection criteria.

Engineering multi-level overlay graphs for shortest-path queries

Computing a shortest path from one node to another in a directed graph is a very common task in practice. This problem is classically solved by Dijkstra’s algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality of the solution can still be guaranteed. In most studies, such techniques are considered individually. The focus of our work is the combination of speed-up techniques for Dijkstra’s algorithm. We consider all possible combinations of four known techniques, namely goal-directed search, bi-directed search, multi-level approach, and shortest-path bounding boxes, and show how these can be implemented. In an extensive experimental study we compare the performance of different combinations and analyze how the techniques harmonize when applied jointly. Several real-world graphs from road maps and public transport and two types of generated random graphs are taken into account.

Combining Speed-Up Techniques for Shortest-Path Computations

We consider a generalization of the shortest-path problem: given an alphabet Σ, a graph Gwhose edges are weighted and Σ-labeled, and a regular language L? Σ*, the L-constrained shortest-path problemconsists of finding a shortest path pin Gsuch that the concatenated labels along pform a word of L. This definition allows to model, e. g., many traffic-planning problems. We present extensions of well-known speed-up techniques for the standard shortest-path problem, and conduct an extensive experimental study of their performance with various networks and language constraints. Our results show that depending on the network type, both goal-directed and bidirectional search speed up the search considerably, while combinations of these do not.

Martin Holzer

Papers

Engineering multilevel overlay graphs for shortest-path queries

Combining speed-up techniques for shortest-path computations

Engineering multi-level overlay graphs for shortest-path queries

Combining Speed-Up Techniques for Shortest-Path Computations

Engineering Label-Constrained Shortest-Path Algorithms