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

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Citations: | 53 - 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 ...tainer has to be calculated offline, but needs only constant space for its orientation and dimensions. Smallest Enclosing Parallelogram. Toussaint’s idea to use rotating calipers has been extended i=-=n [20]-=- to find the smallest enclosing parallelogram. Space consumption is constant and the algorithm is offline. Convex Hull. The convex hull does not fulfill our requirement that containers must be of cons... |

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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 ...erred. 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], 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 plannin... |

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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 |