Keywords and Synonyms
Dilation; t-spanners
Problem Definition
Consider a set S of n points in d-dimensional Euclidean space. A network on S can be modeled as an undirected graph G with vertex set S of size n and an edge set E where every edge (u, v) has a weight. A geometric (Euclidean) network is a network where the weight of the edge (u, v) is the Euclidean distance |uv| between its endpoints. Given a real number \( { t > 1 } \) we say that G is a t-spanner for S, if for each pair of points \( { u,v \in S } \), there exists a path in G of weight at most t times the Euclidean distance between u and v. The minimum t such that G is a t-spanner for S is called the stretch factor, or dilation, of G. For a more detailed description of the construction of t-spanners see the book by Narasimhan and Smid [18]. The problem considered is the construction of t-spanners given a set S of n points in \( { \mathcal{R}^d } \) and a positive real value \( { t > 1 } \), where dis a constant. The aim...
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Gudmundsson, J., Narasimhan, G., Smid, M. (2008). Geometric Spanners. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_167
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