Data compression graph theory

  • What are the methods of graph compression?

    State-of-the-art compression methods broadly fall into two categories: (a) sparsification (removing edges) and (b) coarsening (merging vertices).
    These methods measure spectral similarity between the original graph and a compressed representation in terms of a (inverse) Laplacian quadratic form [12, 13, 14, 15, 16]..

  • What is a compression of a graph?

    A transformation in which all distances on the coordinate plane are shortened by multiplying either all x-coordinates (horizontal compression) or all y-coordinates (vertical compression) of a graph by a common factor less than 1..

  • What is graph compression?

    When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function.
    If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression..

  • A transformation in which all distances on the coordinate plane are shortened by multiplying either all x-coordinates (horizontal compression) or all y-coordinates (vertical compression) of a graph by a common factor less than 1.
Graph compression applies various encoding techniques so that the resultant graph needs lesser storage space. Graph summarization aggregates nodes having similar structural properties/patterns to represent a graph with reduced main memory requirements.
Discrete Morse theory is a combinatorial adaptation of Morse theory developed by Robin Forman.
The theory has various practical applications in diverse fields of applied mathematics and computer science, such as configuration spaces, homology computation, denoising, mesh compression, and topological data analysis.

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