
How to solve an NP-complete problem in linear time - sinab
https://liorpachter.wordpress.com/2019/06/21/how-to-solve-an-np-complete-problem-in-linear-time/
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olliej
It sounds (towards the end) that this is saying that accepting a approximation
of correct is often good enough, and that can often be made polynomial time.

Which is of course correct. There are lots of algorithms where there exist
theoretical minimum complexities, but good approximations can do far better:
lossy compression for example vastly beats the Shannon limit, google maps
doesn’t take decades to plot a route from San Francisco to New York, etc

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bottombutton
You might even luck out with those heuristics. Simulated annealing often
results in the shortest/best/lowest-energy-state solution by accident.

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olliej
Even simpler: ratchet up Joey quality you can easily get lossless output while
technically beating Shannon (because the “average” image in information theory
is noise, and even at the highest quality levels jpeg loses accuracy on them)

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olliej
Haha even better: compress images by just recording the dimensions and average
color. Very high compression, and it’s correct for mono-colour images :)

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bkberry352
In the unlikely situation that you skipped to the comments without reading the
linked article, the solution is to not solve the exact NP-complete problem
since 99.95+% of the time, the linear time approximation algorithm is
sufficient.

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jsnider3
Words cannot express how skeptical I am.

If noone writes a rebuttal to this within a week, I will accept that it might
plausibly be able to do what the title claims.

Edit:

Actually, it seems like the claim in the article is different from the claim
in the title. That's misleading.

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votepaunchy
Demonstrates a clear lack of understanding of NP-completeness.

From the blog: "There is a million dollar prize on offer for a solution to the
P vs. NP problem, so it’s understandable that one may wonder whether this blog
post is an official entry. It is not."

From [1]: "If any NP-complete problem has a polynomial time algorithm, all
problems in NP do."

[1] [https://en.wikipedia.org/wiki/NP-
completeness](https://en.wikipedia.org/wiki/NP-completeness)

