How to solve an NP-complete problem in linear time | Hacker News Reader

How to solve an NP-complete problem in linear time

liorpachter.wordpress.com

12 pointssinab7 comments

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

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

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)

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

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.

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.

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

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