We study the point-to-point shortest path problem in a setting where preprocessing is allowed. We improve the reach-based approach of Gutman [16] in several ways. In particular, we introduce a bidirectional version of the algorithm that uses implicit lower bounds and we add shortcut arcs which reduce vertex reaches. Our modifications greatly reduce both preprocessing and query times. The resulting algorithm is as fast as the best previous method, due to Sanders and Schultes [27]. However, our algorithm is simpler and combines in a natural way with A∗ search, which yields significantly better query times.

In this paper, we consider Dijkstra's algorithm for the single source single target shortest paths problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. For the result of the preprocessing, we admit at most linear space. We assume that a layout of the graph is given. From this layout, in the preprocessing, we determine for each edge a geometric object containing all nodes that can be reached on a shortest path starting with that edge. Based on these geometric objects, the search space for online computation can be reduced significantly. We present an extensive experimental study comparing the impact of different types of objects. The test data we use are traffic networks, the typical field of application for this scenario.

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.

A fundamental approach in finding efficiently best routes or optimal itineraries in traffic information systems is to reduce the search space (part of graph visited) of the most commonly used shortest path routine (Dijkstra’s algorithm) on a suitably defined graph. We investigate reduction of the search space while simultaneously retaining data structures, created during a preprocessing phase, of size linear (i.e., optimal) to the size of the graph. We show that the search space of Dijkstra’s algorithm can be significantly reduced by extracting geometric information from a given layout of the graph and by encapsulating precomputed shortest path information in resulted geometric objects (containers). We present an extensive experimental study comparing the impact of different types of geometric containers using test data from real-world traffic networks. We also present new algorithms as well as an empirical study for the dynamic case of this problem, where edge weights are subject to change and the geometric containers have to be updated, and show that our new methods are 2 to 3 times faster than recomputing everything from scratch. Finally, we discuss the software framework that we developed to realize the implementations of all of our variants of Dijkstra’s algorithm. Such a framework is not trivial to achieve as our goal was to maintain a common code base that is at the same time small, efficient, and flexible, as we wanted to enhance and combine several variants in any possible way.

Using a set of geometric containers to speed up shortest path queries in a weighted graph has been proven a useful tool for dealing with large sparse graphs. Given a layout of a graph G = (V, E), we store, for each edge (u, v) E, the bounding box of all nodes t V for which a shortest u-t-path starts with (u, v). Shortest path queries can then be answered by Dijkstra's algorithm restricted to edges where the corresponding bounding box contains the target.

Abstract. This is a survey of some recent results on point-to-point shortest path algorithms. This classical optimization problem received a lot of attention lately and significant progress has been made. After an overview of classical results, we study recent heuristics that solve the problem while examining only a small portion of the input graph; the graph can be very big. Note that the algorithms we discuss find exact shortest paths. These algorithms are heuristic because they perform well only on some graph classes. While their performance has been good in experimental studies, no theoretical bounds are known to support the experimental observations. Most of these algorithms have been motivated by finding paths in large road networks. We start by reviewing the classical Dijkstra’s algorithm and its bidirectional variant, developed in 1950’s and 1960’s. Then we review A* search, an AI technique developed in 1970’s. Next we turn our attention to modern results which are based on preprocessing the graph. To be practical, preprocessing needs to be reasonably fast and not use too much space. We discuss landmark- and reach-based algorithms as well as their combination. 1