File:Bound on matrix multiplication omega over time.svg

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Original file (SVG file, nominally 380 × 340 pixels, file size: 51 KB)

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Summary

Description
English: The bound on the matrix multiplication exponent ω over time. Based on the account given in the introduction of Williams' paper.


Breaking the Coppersmith-Winograd barrier[1], 2011
Date
Source Own work
Author Self
Other versions

[edit]

  • English (original)
    English (original)
  • Ukrainian
    Ukrainian
SVG development
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 The SVG code is valid.
 This diagram was created with Mathematica.
Source code
InfoField

Mathematica code

plotRange = {{1950, 2015}, {2.32, 3.01}};
data = {{1950, 3}, {1968, 3}, {1969, 2.808}, {1978, 2.796}, {1979, 2.78}, {1980.5, 2.522}, {1981, 2.517}, {1981.5, 2.496}, {1986, 2.479}, {1990, 2.376}, {2010, 2.374}, {2012, 2.373}};
dataPlot = ListPlot[data, Joined -> True, Mesh -> All, PlotRange -> plotRange];
labelData = {{"naive", {1959, 2.985}}, {"Strassen", {1964, 2.825}}, {"Pan", {1976, 2.815}}, {"Bini et al.", {1985.5, 2.78}}, {"Schönhage", {1974, 2.53}}, {"Romani", {1986, 2.52}}, {"Coppersmith-Winograd", {1967.5, 2.49}}, {"Strassen", {1991.3, 2.48}}, {"Coppersmith-Winograd", {1975.5, 2.393}}, {"Stothers", {2005, 2.39}}, {"Williams", {2010, 2.36}}};
labels = Text[#[[1]], #[[2]]] & /@ labelData;
Show[dataPlot, Graphics[{Black, labels}], PlotRange -> plotRange, GridLines -> Automatic, GridLinesStyle -> Directive[Opacity[0.6], Dashed], AxesLabel -> {"Year", "\[Omega]"}, AspectRatio -> 1]
After saving the file to an SVG, edit the raw SVG to (1) always use the Times font, (2) improve the placement of labels including merging each label in to a single text tag, and (3) add "width='360' height='340'" to the end of the SVG tag. The 2014 bound was also added by manual edition of the SVG (so it is not reflected in the above code).

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

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inception

17 August 2012

media type

image/svg+xml

checksum

c950caf71416395b09d815a9114b4f6b03538846

determination method or standard: SHA-1

data size

51,980 byte

height

340 pixel

width

380 pixel

File history

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Date/TimeThumbnailDimensionsUserComment
current22:46, 15 October 2019Thumbnail for version as of 22:46, 15 October 2019380 × 340 (51 KB)wikimediacommons>A3nmAdd 2014 bound by Le Gall. Edited SVG file directly using Inkscape -- I didn't use Mathematica, so the provided source code is no longer valid.

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