PReaCH: A Fast Lightweight Reachability Index using Pruning and Contraction Hierarchies

We develop the data structure PReaCH (for Pruned Reachability Contraction Hierarchies) which supports reachability queries in a directed graph, i.e., it supports queries that ask whether two nodes in the graph are connected by a directed path. PReaCH adapts the contraction hierarchy speedup techniques for shortest path queries to the reachability setting. The resulting approach is surprisingly simple and guarantees linear space and near linear preprocessing time. Orthogonally to that, we improve existing pruning techniques for the search by gathering more information from a single DFS-traversal of the graph. PReaCH-indices significantly outperform previous data structures with comparable preprocessing cost. Methods with faster queries need significantly more preprocessing time in particular for the most difficult instances

Compressed Transmission of Route Descriptions

We present two methods to compress the description of a route in a road network, i.e., of a path in a directed graph. The first method represents a path by a sequence of via edges. The subpaths between the via edges have to be unique shortest paths. Instead of via edges also via nodes can be used, though this requires some simple preprocessing. The second method uses contraction hierarchies to replace subpaths of the original path by shortcuts. The two methods can be combined with each other. Also, we propose the application to mobile server based routing: We compute the route on a server which has access to the latest information about congestions for example. Then we transmit the computed route to the car using some mobile radio communication. There, we apply the compression to save costs and transmission time. If the compression works well, we can transmit routes even when the bandwidth is low. Although we have not evaluated our ideas with realistic data yet, they are quite promising.Comment: 7 pages, technical repor

Comparative Study of Speed-Up Routing Algorithms in Road Networks

We study the problem of finding the shortest distance and the shortest path from one node to another in graphs modeling large road networks. Classical algorithms like Dijkstra and Astar do not have good performance in such networks. In recent years, two new approaches called Contraction Hierarchy and Hub Labeling which use preprocessing to generate auxiliary data to improve the query time performance were proposed, and many variants have followed. These algorithms are very efficient on large networks when a large number of queries is expected. In the literature, these algorithms are called speed-up algorithms. More recently, dynamic routing algorithms have been proposed, such as Customizable Contraction Hierarchy and Dynamic Hierarchical Hub Labeling. These are designed to respond efficiently to edge weight changes resulting from changes in traffic. In this thesis, we present an experimental study of the performance of the above static and dynamic routing algorithms on two different road networks, in terms of travel time and query processing time. Our results show that Customizable Contraction Hierarchy is the best for shortest path query in both the static and dynamic settings, while Hub Labeling is the most efficient in answering shortest distance queries in the static setting. We also show that Dynamic Hub Labeling’s edge weight update operations are inefficient in practice

Fast Detour Computation for Ride Sharing

Todays ride sharing services still mimic a better billboard. They list the offers and allow to search for the source and target city, sometimes enriched with radial search. So finding a connection between big cities is quite easy. These places are on a list of designated origin and distination points. But when you want to go from a small town to another small town, even when they are next to a freeway, you run into problems. You can't find offers that would or could pass by the town easily with little or no detour. We solve this interesting problem by presenting a fast algorithm that computes the offers with the smallest detours w.r.t. a request. Our experiments show that the problem is efficiently solvable in times suitable for a web service implementation. For realistic database size we achieve lookup times of about 5ms and a matching rate of 90% instead of just 70% for the simple matching algorithms used today.Comment: 5 pages, 2 figure environment, 4 includegraphic