Keywords and Synonyms
Stretch factor
Problem Definition
Given a geometric graph in d-dimensional space, it is useful to preprocess it so that distance queries, exact or approximate, can be answered efficiently. Algorithms that can report distance queries in constant time are also referred to as “distance oracles”. With unlimited preprocessing time and space, it is clear that exact distance oracles can be easily designed. This entry sheds light on the design of approximate distance oracles with limited preprocessing time and space for the family of geometric graphs with constant dilation.
Notation and Definitions
If p and q are points in ℝd, then the notation |pq| is used to denote the Euclidean distance between p and q; the notation \( \delta_G(p,q) \) is used to denote the Euclidean length of a shortest path between p and q in a geometric network G. Given a constant \( t \mathchar"313E 1 \), a graph G with vertex set S is a t-spanner for S if \( \delta_G(p,q) \leq t |pq| \)for any...
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Gudmundsson, J., Narasimhan, G., Smid, M. (2008). Applications of Geometric Spanner Networks. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_15
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