@inproceedings{f66a2cca35474cfbbb986aa1a61ed267,

title = "Approximate distance queries in disk graphs",

abstract = "We present efficient algorithms for approximately answering distance queries in disk graphs. Let G be a disk graph with n vertices and m edges. For any fixed ε > 0, we show that G can be preprocessed in O(m√nε-1 + mε-2 log S) time, constructing a data structure of size O(n3/2ε-1 + nε-2 log S), such that any subsequent distance query can be answered approximately in O(√nε-1+ε-2log S) time. Here S is the ratio between the largest and smallest radius. The estimate produced is within an additive error which is only e times the longest edge on some shortest path. The algorithm uses an efficient subdivision of the plane to construct a sparse graph having many of the same distance properties as the input disk graph. Additionally, the sparse graph has a small separator decomposition, which is then used to answer distance queries. The algorithm extends naturally to the higher dimensional ball graphs.",

author = "Martin F{\"u}rer and Kasiviswanathan, {Shiva Prasad}",

year = "2007",

doi = "10.1007/11970125_14",

language = "English (US)",

isbn = "9783540695134",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "174--187",

booktitle = "Approximation and Online Algorithms - 4th International Workshop, WAOA 2006, Revised Papers",

address = "Germany",

note = "4th Workshop on Approximation and Online Algorithms, WAOA 2006 ; Conference date: 14-09-2006 Through 15-09-2006",

}