The Quanta article on the paper was considerably more breathless in describing a fine piece of work in mathematics. The author here points out that one of the things that makes Dijkstra's result iconic is that it could be used practically in a straightforward way. As an engineer, beautiful mathematics is useless if I can't convert it to running code.
Actually there's a whole bunch of mathematics which I find useful as an engineer because it tells me that the perfection I have vaguely imagined I could reach for is literally not possible and so I shouldn't expend any effort on that.
e.g Two body gravity I can just do the math and get exact answers out. But for N> 2 bodies that doesn't work and it's not that I need to think a bit harder, maybe crack out some graduate textbooks to find a formula, if I did hopefully the grad books say "Three body problem generally not amenable to solution". I will need to do an approximation, exact answers are not available (except in a few edge cases).
> Actually there's a whole bunch of mathematics which I find useful as an engineer because it tells me that the perfection I have vaguely imagined I could reach for is literally not possible and so I shouldn't expend any effort on that
That's actually given as a reason to study NP-completeness in the classic 1979 book "Computers and Intractability: A Guide to the Theory of NP-Completeness" by Garey & Johnson, which is one of the most cited references in computer science literature.
Chapter one starts with a fictional example. Say you have been trying to develop an algorithm at work that validates designs for new products. After much work you haven't found anything better than exhaustive search, which is too slow.
You don't want to tell your boss "I can't find an efficient algorithm. I guess I'm just too dumb".
What you'd like to do is prove that the problem is inherently intractable, so you could confidently tell your boss "I can't find an efficient algorithm, because no such algorithm is possible!".
Unfortunately, the authors note, proving intractability is also often very hard. Even the best theoreticians have been stymied trying to prove commonly encountered hard problems are intractable. That's where the book comes in:
> However, having read this book, you have discovered something almost as good. The theory of NP-completeness provides many straightforward techniques for proving that a given problem is “just as hard” as a large number of other problems that are widely recognized as being difficult and that have been confounding the experts for years.
Using the techniques from the book you prove the problem is NP-complete. Then you can go to your boss and announce "I can't find an efficient algorithm, but neither can all these famous people". The authors note that at the very least this informs your boss that it won't do any good to fire you and hire another algorithms expert. They go on:
> Of course, our own bosses would frown upon our writing this book if its sole purpose was to protect the jobs of algorithm designers. Indeed, discovering that a problem is NP-complete is usually just the beginning of work on that problem.
...
> However, the knowledge that it is NP-complete does provide valuable information about what lines of approach have the potential of being most productive. Certainly the search for an efficient, exact algorithm should be accorded low priority. It is now more appropriate to concentrate on other, less ambitious, approaches. For example, you might look for efficient algorithms that solve various special cases of the general problem. You might look for algorithms that, though not guaranteed to run quickly, seem likely to do so most of the time. Or you might even relax the problem somewhat, looking for a fast algorithm that merely finds designs that meet most of the component specifications. In short, the primary application of the theory of NP-completeness is to assist algorithm designers in directing their problem-solving efforts toward those approaches that have the greatest likelihood of leading to useful algorithms.
That might reduce botting for about 30 days, people will just tee up an endless supply of parked ids that will then spin up to post after the lockout expires.
Not just subscription farming, you cannot use the latest mobile app versions without agreeing to data mining. Their business model now is literally collecting user health and usage data to resell to other companies and of course for AI training. Avoid.
Genshin is produced by a Chinese company, MiHoYo. And I think Monotype will have a much harder time trying to strongarm a PRC-based company if they decide to try this there.
> Monotype will have a much harder time trying to strongarm a PRC-based company if they decide to try this there
Monotype has a Chinese subsidiary [0] which has worked with Chinese champions like Tencent [1] and Alibaba [2].
As long as a foreign vs Chinese business dispute doesn't involve a national champion or a very politically connected Chinese firm (or the foreign company made a partnership with a politically connected partner) the dispute is somewhat fair.
While China's leadership is trying to build self-sufficiency, it is also still trying to attract foreign companies to China and prevent an FDI outflow [3], and that requires some level of impartiality in contract disputes. China is not as economically isolated as Russia is today - though even Russian authorities tend to only use the heavy hammer against American and European companies as can be seen with the continued operation of Japanese, Korean, Taiwanese, Vietnamese, and Indian firms in Russia despite the risk of sanctions.
a fairly large number - a bigger question is what happens to all the CO buildings once all the copper is turned down.
There is a huge opportunity about 5 years from now for edge datacenters. You have these buildings which have highly reliable power and connectivity, all thats needed is servers which can live in a NEBS environment.
Most of those CO's are in buildings that don't have all that much space in them, were built in the 40's and 50's, and likely aren't suitable for that kind of thing. Cooling would be a big deal.
I have been in ~15 CO's - there is tons of floor space in them, and the only thing telephone switching equipment has done since the 50's is shrink - beyond that, most existing CO buildings had expansions when electronic switching came about, because they couldnt add the new electronic (1/1A/5 ESS) without additional floor space. Cooling is noted by the requirement for NEBS compliant equipment.
Central offices are everywhere, too. You've driven or walked by any number of them, and the most you noticed was a Bell System logo. The downtown COs in big cities are on expensive real estate.
I want to know so badly what the telcos are still doing with all that space. Some, like mentioned above, are probably edge data centers. I imagine there's a lot of Internet infrastructure in them as well.
But even the biggest IXP is surely tiny compared to the space required for an electromechanical exchange (that would host human operators as well). Are there just floors and floors of empty space? Like you said, on very expensive downtown real estate?
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