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The compressed exponential function (with β > 1) has less practical importance, with the notable exceptions of β = 2, which gives the normal distribution, and of compressed exponential relaxation in the dynamics of amorphous solids. [1] In mathematics, the stretched exponential is also known as the complementary cumulative Weibull distribution.
Power graph analysis is the computation, analysis and visual representation of a power graph from a graph . Power graph analysis can be thought of as a lossless compression algorithm for graphs. [1] It extends graph syntax with representations of cliques, bicliques and stars.
Bipartite network projection is an extensively used method for compressing information about bipartite networks. [1] Since the one-mode projection is always less informative than the original bipartite graph, an appropriate method for weighting network connections is often required. Optimal weighting methods reflect the nature of the specific ...
There are functions for which the graph size is always exponential—independent of variable ordering. This holds e.g. for the multiplication function. [ 1 ] In fact, the function computing the middle bit of the product of two n {\displaystyle n} -bit numbers does not have an OBDD smaller than 2 ⌊ n / 2 ⌋ / 61 − 4 {\displaystyle 2 ...
Another graph parameter, the rank-width, is bounded in both directions by the clique-width: rank-width ≤ clique-width ≤ 2 rank-width + 1. [12] Additionally, if a graph G has clique-width k, then the graph power G c has clique-width at most 2kc k. [13] Although there is an exponential gap in both the bound for clique-width from treewidth and ...
Thus, a representation that compresses the storage size of a file from 10 MB to 2 MB yields a space saving of 1 - 2/10 = 0.8, often notated as a percentage, 80%. For signals of indefinite size, such as streaming audio and video, the compression ratio is defined in terms of uncompressed and compressed data rates instead of data sizes:
In mathematics, the graph Fourier transform is a mathematical transform which eigendecomposes the Laplacian matrix of a graph into eigenvalues and eigenvectors.Analogously to the classical Fourier transform, the eigenvalues represent frequencies and eigenvectors form what is known as a graph Fourier basis.
Lengauer and Tarjan developed an algorithm which is almost linear, [1] and in practice, except for a few artificial graphs, the algorithm and a simplified version of it are as fast or faster than any other known algorithm for graphs of all sizes and its advantage increases with graph size. [9]