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File:Bound on matrix multiplication omega over time.svg

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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
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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).

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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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current20:46, 15 October 2019Thumbnail for version as of 20:46, 15 October 2019380 × 340 (51 KB)A3nm (talk | contribs)Add 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.
13:48, 17 August 2012Thumbnail for version as of 13:48, 17 August 2012360 × 340 (37 KB)Bender2k14 (talk | contribs){{Information |Description ={{en|1=The bound of the matrix multiplication exponent omega over time. Based on the account given in the introduction of Williams' paper. {{Citation | last1=Williams | first1=Virginia | title=Breaking the Coppersmith-W...

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