## Geometric Speed-Up Techniques for Finding Shortest Paths in Large Sparse Graphs (2003)

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Citations: | 54 - 14 self |

### BibTeX

@MISC{Wagner03geometricspeed-up,

author = {Dorothea Wagner and Thomas Willhalm},

title = {Geometric Speed-Up Techniques for Finding Shortest Paths in Large Sparse Graphs},

year = {2003}

}

### Years of Citing Articles

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### Abstract

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.

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Citation Context ...26] can be integrated by reverting all edges and running the preprocessing a second time. Space and time consumption for the preprocessing simply doubles. – In combination with a multi-level approac=-=h [27,2],-=- one constructs a graph containing all levels and inter-level edges first. The geometric pruning is then performed on this graph. Acknowledgment We thank Jasper Möller for his help in implementing an... |

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Citation Context ...26] can be integrated by reverting all edges and running the preprocessing a second time. Space and time consumption for the preprocessing simply doubles. – In combination with a multi-level approac=-=h [27,2],-=- one constructs a graph containing all levels and inter-level edges first. The geometric pruning is then performed on this graph. Acknowledgment We thank Jasper Möller for his help in implementing an... |

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Citation Context ...anguage constraints and changes over time. Modeling an (interactive) travel information system for scheduled transport is covered by [12] and [13], and a multi-criteria implementation is presented in =-=[14]-=-. A distributed system which integrates multiple transport providers has been realized in [15]. One of the features of travel planning (independant of the vehicle type) is the fact that the network do... |

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Citation Context ...bel correcting algorithms were compared in respect to single source single target shortest path computations. They conclude that for shorter paths a label correcting algorithm should be preferred. In =-=[11]-=- Barrett et al. present a system that covers formal language constraints and changes over time. Modeling an (interactive) travel information system for scheduled transport is covered by [12] and [13],... |

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Citation Context ... The application of shortest path computations in travel networks is also widely covered by the literature: [9] compares different algorithms to compute shortest paths trees in real road networks. In =-=[10] t-=-he two best label setting ⋆ This work was partially supported by the Human Potential Programme of the European Union under contract no. HPRN-CT-1999-00104 (AMORE) and and by the DFG under grant WA 6... |

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Citation Context .... Algorithms with average case linear time are known for edge weights uniformly distributed in the interval [0, 1] [6] and for edge weights uniformly distributed in {1, . . . , M} [7]. A recent study =-=[8]-=- shows that the sorting bottleneck can be also avoided in practice for undirected graphs. The application of shortest path computations in travel networks is also widely covered by the literature: [9]... |

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Citation Context ...respond to the layout. They havesbetween 409 nodes (Netherlands) and 6884 nodes (Germany) but are not as sparse as the street graphs. All test sets were converted to the XML-based GraphML file format =-=[22]-=- to allow us a unified processing. We sampled random single source single target queries to determine the average number of nodes that are visited by the algorithm. The sampling was done until the len... |

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Citation Context ...al priority queue such as [6,7] can easily be combined with it. The decrease of the search space is in fact the same (but the actual running time would be different of course). – Goal-directed searc=-=h [23] or A -=-∗ has been shown in [24,25] to be very useful for transportation networks. As it simply modifies the edge weights, a combination of geometric pruning and A ∗ can be realized straight forward. – ... |

1 | Shortest paths in euclidean space - Scdgcwick, Vittcr - 1986 |

1 | Smallest enclosing disks (balls and ellipsoids - Wclzl - 1991 |