arXiv subjects

Tim Zeitz

Publications and source records attributed to Tim Zeitz.

6 recordsLinked to original sources

arXiv2025

Customizable Contraction Hierarchies -- A Survey

This work establishes the technical fundamentals of a well-tuned Customizable Contraction Hierarchies (CCH) implementation that is simple and elegant. We give a detailed overview of the state of the art of CCH, review recent advances on CCH and show how to combine them. Additionally, we propose further refinements that improve the performance of CCH. An extensive evaluation confirms that a CCH framework is not only comprehensive in supported features but also competitive in performance to both Contraction Hierarchies (CH) and Customizable Route Planning (CRP).

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arXiv2022

Combining Predicted and Live Traffic with Time-Dependent A* Potentials

We study efficient and exact shortest path algorithms for routing on road networks with realistic traffic data. For navigation applications, both current (i.e., live) traffic events and predictions of future traffic flows play an important role in routing. While preprocessing-based speedup techniques have been employed successfully to both settings individually, a combined model poses significant challenges. Supporting predicted traffic typically requires expensive preprocessing while live traffic requires fast updates for regular adjustments. We propose an A*-based solution to this problem. By generalizing A* potentials to time dependency, i.e. the estimate of the distance from a vertex to the target also depends on the time of day when the vertex is visited, we achieve significantly faster query times than previously possible. Our evaluation shows that our approach enables interactive query times on continental-sized road networks while allowing live traffic updates within a fraction of a minute. We achieve a speedup of at least two orders of magnitude over Dijkstra's algorithm and up to one order of magnitude over state-of-the-art time-independent A* potentials.

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arXiv2020

Efficient Route Planning with Temporary Driving Bans, Road Closures, and Rated Parking Areas

We study the problem of planning routes in road networks when certain streets or areas are closed at certain times. For heavy vehicles, such areas may be very large since many European countries impose temporary driving bans during the night or on weekends. In this setting, feasible routes may require waiting at parking areas, and several feasible routes with different trade-offs between waiting and driving detours around closed areas may exist. We propose a novel model in which driving and waiting are assigned abstract costs, and waiting costs are location-dependent to reflect the different quality of the parking areas. Our goal is to find Pareto-optimal routes with regards to arrival time at the destination and total cost. We investigate the complexity of the model and determine a necessary constraint on the cost parameters such that the problem is solvable in polynomial time. We present a thoroughly engineered implementation and perform experiments on a production-grade real world data set. The experiments show that our implementation can answer realistic queries in around a second or less which makes it feasible for practical application.

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arXiv2019

A Fast and Tight Heuristic for A* in Road Networks

We study exact, efficient and practical algorithms for route planning in large road networks. Routing applications often require integrating the current traffic situation, planning ahead with traffic predictions for the future, respecting forbidden turns, and many other features depending on the exact application. While Dijkstra's algorithm can be used to solve these problems, it is too slow for many applications. A* is a classical approach to accelerate Dijkstra's algorithm. A* can support many extended scenarios without much additional implementation complexity. However, A*'s performance depends on the availability of a good heuristic that estimates distances. Computing tight distance estimates is a challenge on its own. On road networks, shortest paths can also be quickly computed using hierarchical speedup techniques. They achieve speed and exactness but sacrifice A*'s flexibility. Extending them to certain practical applications can be hard. In this paper, we present an algorithm to efficiently extract distance estimates for A* from Contraction Hierarchies (CH), a hierarchical technique. We call our heuristic CH-Potentials. Our approach allows decoupling the supported extensions from the hierarchical speed-up technique. Additionally, we describe A* optimizations to accelerate the processing of low degree nodes, which often occur in road networks.

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arXiv2019

Space-Efficient, Fast and Exact Routing in Time-Dependent Road Networks

We study the problem of quickly computing point-to-point shortest paths in massive road networks with traffic predictions. Incorporating traffic predictions into routing allows, for example, to avoid commuter traffic congestions. Existing techniques follow a two-phase approach: In a preprocessing step, an index is built. The index depends on the road network and the traffic patterns but not on the path start and end. The latter are the input of the query phase, in which shortest paths are computed. All existing techniques have large index size, slow query running times or may compute suboptimal paths. In this work, we introduce CATCHUp (Customizable Approximated Time-dependent Contraction Hierarchies through Unpacking), the first algorithm that simultaneously achieves all three objectives.The core idea of CATCHUp is to store paths instead of travel times at shortcuts. Shortcut travel times are derived lazily from the stored paths. We perform an experimental study on a set of real world instances and compare our approach with state-of-the-art techniques. Our approach achieves the fastest preprocessing, competitive query running times and up to 38 times smaller indexes than competing approaches.

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arXiv2017

Distributed Graph Clustering using Modularity and Map Equation

We study large-scale, distributed graph clustering. Given an undirected graph, our objective is to partition the nodes into disjoint sets called clusters. A cluster should contain many internal edges while being sparsely connected to other clusters. In the context of a social network, a cluster could be a group of friends. Modularity and map equation are established formalizations of this internally-dense-externally-sparse principle. We present two versions of a simple distributed algorithm to optimize both measures. They are based on Thrill, a distributed big data processing framework that implements an extended MapReduce model. The algorithms for the two measures, DSLM-Mod and DSLM-Map, differ only slightly. Adapting them for similar quality measures is straight-forward. We conduct an extensive experimental study on real-world graphs and on synthetic benchmark graphs with up to 68 billion edges. Our algorithms are fast while detecting clusterings similar to those detected by other sequential, parallel and distributed clustering algorithms. Compared to the distributed GossipMap algorithm, DSLM-Map needs less memory, is up to an order of magnitude faster and achieves better quality.

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