Episode 589
Geometric spanner Fri, 2018Dec14 00:08 UTC Length  2:06
Direct Link Welcome to random Wiki of the Day where we read the summary of a random Wikipedia page every day.
The random article for Friday, 14 December 2018 is Geometric spanner.
A geometric spanner or a tspanner graph or a tspanner was initially introduced as a weighted graph over a set of points as its vertices for which there is a tpath between any pair of vertices for a fixed parameter t. A tpath is defined as a path through the graph with weight at most t times the spatial distance between its endpoints. The parameter t is called the stretch factor or dilation factor of the spanner.In computational geometry, the concept was first discussed by L.P. Chew in 1986, although the term "spanner" was not used in the original paper.
The notion of graph spanners has been known in graph theory: tspanners are spanning subgraphs of graphs with similar dilation property, where distances between graph vertices are defined in graphtheoretical terms. Therefore geometric spanners are graph spanners of complete graphs embedded in the plane with edge weights equal to the distances between the embedded vertices in the corresponding metric.
Spanners may be used in computational geometry for solving some proximity problems. They have also found applications in other areas, such as in motion planning, in telecommunication networks: network reliability, optimization of roaming in mobile networks, etc.
This recording reflects the Wikipedia text as of 00:08 UTC on Friday, 14 December 2018.
For the full current version of the article, go to http://en.wikipedia.org/wiki/Geometric_spanner.
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