
Theorists Draw Closer to Perfect Coloring - signa11
https://www.quantamagazine.org/20151020-perfect-graph-coloring/
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danbruc
If I understand it correctly a polynomial time algorithm for coloring perfect
graphs has been found in 1984 [1] but the algorithm is no good in practice,
i.e. it suffers from numerical instability. So this is probably about the
search for a practical algorithm.

[1]
[http://www.zib.eu/groetschel/pubnew/paper/groetschellovaszsc...](http://www.zib.eu/groetschel/pubnew/paper/groetschellovaszschrijver1984b.pdf)

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shoo
If possible, could you please go into a bit more detail regarding numerical
instability? Is the instability a general hazard with the ellipsoid method, or
particular to to the Gr\"{o}tschel et al algorithms?

I've heard of the odd occasion where there is a common belief that an old
algorithm does not perform well in practice, based on older experimental
studies, but it turns out that the algorithm is actually quite effective, but
perhaps only when combined with a few other good implementation decisions.

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danbruc
That is far beyond my knowledge of graph theory and convex optimization but
the Wikipedia article [1] suggests that is a general problem of the method and
it only works well for low dimensional data.

[1]
[https://en.wikipedia.org/wiki/Ellipsoid_method#Performance](https://en.wikipedia.org/wiki/Ellipsoid_method#Performance)

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mcherm
It is rare -- nearly unheard of -- that an active area of mathematical
research would be simple enough to explain to a bright 9-yr-old. But this
probably is. (Concepts: graph, coloring, max colors needed, clique... that's
about it.) I think I'll try it with my kids.

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cschmidt
You'll probably be interested in this guy, who does graph coloring problems
for 7 year old kids. He even has coloring books:

[http://jdh.hamkins.org/math-for-seven-year-olds-graph-
colori...](http://jdh.hamkins.org/math-for-seven-year-olds-graph-coloring-
chromatic-numbers-eulerian-paths/)

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lumpypua
Awesome article, thank you for posting. It's cool to see what's bleeding edge
in math explained in such an approachable way.

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spdustin
The little interactive in the article is practically begging to be made into a
game.

