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The Fastest and Shortest Algorithm for All Well-Defined Problems (2002) (arxiv-vanity.com)
95 points by tosh 72 days ago | hide | past | web | favorite | 14 comments




A selected excerpt from this paper:

"The same should hold for Theorem 1, as will be discussed. We avoid the O(1) notation as far as possible, as it can be severely misleading (e.g. 10^42 = O(1)^O(1)) = O(1)).

This work could be viewed as another O() warning showing, how important factors, and even subdominant additive terms, are."


O() is a notion of speed of growth, not measuring how large are constants.


Right, the critique is evaluating algorithms based solely on asymptotic time / space characteristics is insufficient. Constants can be significant if they are big enough.



From the header of the website:

> arXiv Vanity renders academic papers from arXiv as responsive web pages so you don’t have to squint at a PDF.

Why aren't more PDFs displayed like this on the web? I thought the math stuff would be a problem but this site shows the math stuff alright.

Anyone knows how to reliably convert complex PDFs to beautiful web pages like this?


with arXiv the TeX source is available for download (under the "Other formats" link), which I think is what arXiv-vanity uses. I imagine it would be really tough to go reliably from arbitrary PDF to HTML without screwing up the math and figures.


I mean firefox' built in pdf-reader is javascript based. I imagine it renders to a canvas instead of to html, but it doesn't seem like an impossibility to render to html in any case.


I read scientific PDFs on a daily basis. I never knew that this was a problem.


PDFs can be annoying on a small tablet or phone. It seems like I used to have more display options, but I tried to catch up on some reading on my last flight and I couldn't find an option to reflow the text.


Admittedly, I do not read scientific PDFs on tablets, let alone phones.


The math stuff is not quite alright if you compare it to the PDF. Besides that the PDF is absolutely preferable on iPad Safari.


Indeed. But the reflow and good readability trumps the few mistakes made.


The math stuff is being rendered with a library called MathJax https://www.mathjax.org/




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