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The stretch factor is important in the theory of geometric spanners, weighted graphs that approximate the Euclidean distances between a set of points in the Euclidean plane. In this case, the embedded metric S is a finite metric space, whose distances are shortest path lengths in a graph, and the metric T into which S is embedded is the ...
If an embedding maps all pairs of vertices with distance to pairs of vectors with distance in the range [,] then its stretch factor or distortion is the ratio /; an isometry has stretch factor one, and all other embeddings have greater stretch factor. [1] The graphs that have an embedding with at most a given distortion are closed under graph ...
A t-path 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. [1] In computational geometry, the concept was first discussed by L.P. Chew in 1986, [2] although the term "spanner" was not used in the original ...
Greedy geometric spanner of 100 random points with stretch factor t = 2 Greedy geometric spanner of the same points with stretch factor t = 1.1. In computational geometry, a greedy geometric spanner is an undirected graph whose distances approximate the Euclidean distances among a finite set of points in a Euclidean space.
The stretch factor of the entire spanner is the maximum stretch factor over all pairs of points within it. Recall from above that θ = 2 π / k {\displaystyle \theta =2\pi /k} , then when k ≥ 9 {\displaystyle k\geq 9} , the Θ {\displaystyle \Theta } -graph has a stretch factor of at most 1 / ( cos θ − sin θ ) {\displaystyle 1 ...
For example, the graph of y = A sin(x) + B cos(x) can be obtained from the graph of y = sin(x) by translating it through an angle α along the positive X axis (where tan(α) = A ⁄ B), then stretching it parallel to the Y axis using a stretch factor R, where R 2 = A 2 + B 2.
Redfin, a Seattle, Washington-based real estate giant, forecasts average 30-year fixed mortgage rates will remain in the high 6% range over the duration of 2025. Online real estate marketplace ...
A flow is a process in which the points of a space continuously change their locations or properties over time. More specifically, in a one-dimensional geometric flow such as the curve-shortening flow, the points undergoing the flow belong to a curve, and what changes is the shape of the curve, its embedding into the Euclidean plane determined by the locations of each of its points. [2]