Keywords and Synonyms
Random geometric graphs ; Monotonic properties; Isolated nodes; Connectivity; Gabriel graphs ; Delaunay triangulations ; Greedy forward routing
Problem Definition
Given a point set V, a graph of the vertex set V in which two vertices have an edge if and only if the distance between them is at most r for some positive real number r is called a r-disk graph over the vertex set V and denoted by \( { G_{r}\left(V\right) } \). If \( { r_{1}\leq r_{2} } \), obviously \( { G_{r_{1}}\left(V\right) \subseteq G_{r_{2}}\left(V\right) } \). A graph property is monotonic (increasing) if a graph is with the property, then every supergraph with the same vertex set also has the property. The critical-range problem (or critical‐radius problem) is concerned with the minimal range r such that \( { G_{r}\left(V\right) } \) is with some monotonic property. For example, graph connectivity is monotonic and crucial to many applications. It is interesting to know whether \( {...
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Yi, CW. (2008). Critical Range for Wireless Networks. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_95
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DOI: https://doi.org/10.1007/978-0-387-30162-4_95
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