## Distance Oracles for Spatial Networks

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Citations: | 10 - 4 self |

### BibTeX

@MISC{Sankaranarayanan_distanceoracles,

author = {Jagan Sankaranarayanan and Hanan Samet},

title = {Distance Oracles for Spatial Networks},

year = {}

}

### OpenURL

### Abstract

Abstract — The popularity of location-based services and the need to do real-time processing on them has led to an interest in performing queries on transportation networks, such as finding shortest paths and finding nearest neighbors. The challenge is that these operations involve the computation of distance along a spatial network rather than “as the crow flies. ” In many applications an estimate of the distance is sufficient, which can be achieved by use of an oracle. An approximate distance oracle is proposed for spatial networks that exploits the coherence between the spatial position of vertices and the network distance between them. Using this observation, a distance oracle is introduced that is able to obtain the ε-approximate network distance between two vertices of the spatial network. The network distance between every pair of vertices in the spatial network is efficiently represented by adapting the well-separated pair technique to spatial networks. Initially, use is made of an ε-approximate distance oracle of size O ( n εd) that is capable of retrieving the approximate network distance in O(logn) time using a B-tree. The retrieval time can be theoretically reduced to O(1) time by proposing another ε-approximate distance oracle of size O ( nlogn εd) that uses a hash table. Experimental results indicate that the proposed technique is scalable and can be applied to sufficiently large road networks. A 10%-approximate oracle (ε = 0.1) on a large network yielded an average error of 0.9 % with 90 % of the answers making an error of 2 % or less and an average retrieval time of 68µ seconds. Finally, a strategy for the integration of the distance oracle into any relational database system as well as using it to perform a variety of spatial queries such as region search, k-nearest neighbor search, and spatial joins on spatial networks is discussed. I.

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Citation Context ...e to node distances. The requirement that these distances be computed in real-time precludes the use of conventional graph-based algorithms (e.g., the INE and IER methods [1] and improvements on them =-=[2]-=-, and hierarchical graph methods [3], [4]) which usually incorporate Dijkstra’s shortest-path algorithm [5] in at least some parts of the solution [6]. It is well-known that the problem with Dijkstra’... |

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Citation Context ...ctions of destination vertices. This is done by adapting the notion of a well-separated decomposition of a point set, originally proposed by Callahan and Kosaraju [14] and used by others (e.g., [15], =-=[16]-=-) for a point set, to a spatial network. It is important to note that one of the ways of evaluating the significance of our work lies in determining the extent to which we can improve on the storage c... |

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24 | Efficient query processing on spatial networks - Sankaranarayanan, Alborzi, et al. - 2005 |

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Citation Context ...he quadtree in that context is primarily to take advantage of its dimension-reducing property [11] to decrease the storage requirements instead of for speeding up operations such as ray tracing [12], =-=[13]-=-. The above algorithms exploit the spatial coherence of the destination vertices of the spatial network to reduce the storage requirements of the collection of precomputed shortest pathsProceedings o... |

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Citation Context ...atial networks. Our experiments show γH to be large for road networks. The technique that we propose is similar to the RNE technique of Shahabi et al. [18] (and a recent improvement by Kriegel et al. =-=[19]-=-) who apply a Lipschitz embedding [20] to spatial networks. The RNE technique embeds the vertices of the spatial network in a high-dimensional vector space, such that vertices of the spatial network a... |

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Citation Context ... collections of destination vertices. This is done by adapting the notion of a well-separated decomposition of a point set, originally proposed by Callahan and Kosaraju [14] and used by others (e.g., =-=[15]-=-, [16]) for a point set, to a spatial network. It is important to note that one of the ways of evaluating the significance of our work lies in determining the extent to which we can improve on the sto... |

7 |
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5 |
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Citation Context ...ck would form an internal node. Callahan and Kosaraju’s construction [14] did not incur this problem because they used a fair-split tree which is a data-dependent decomposition. Fischer and Har-Peled =-=[25]-=- remedy this problem through the use of a variant of a pathcompressed quadtree which is obtained from the PR quadtree by compressing such trivial paths into one compressed link. The advantage of the p... |

2 |
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Citation Context ...r with one gigabyte of RAM. We implemented our algorithms using GNU C++. A number of publicly available road network datasets were used in the evaluation. These were obtained from the US Tiger Census =-=[29]-=- and the National Atlas [30] websites. In particular, we used a dataset containing all the major roads in the USA (i.e., more than 380,000 vertices and 400,000 edges). Sample random rectangular region... |

1 |
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Citation Context ...We implemented our algorithms using GNU C++. A number of publicly available road network datasets were used in the evaluation. These were obtained from the US Tiger Census [29] and the National Atlas =-=[30]-=- websites. In particular, we used a dataset containing all the major roads in the USA (i.e., more than 380,000 vertices and 400,000 edges). Sample random rectangular regions were drawn from the datase... |