A landmark paper entitled "Relativisations of the P =? NP Question" by Theodore Baker, John Gill, and Robert Solovay was published in the SIAM Journal of Computing Vol.4, No.4, December 1975.
It talks about the P vs. NP problem and introduces methods of relativisations. I have the paper, but I'd like to know more about testing an algorithm to see if it is relativisable. Where can I find more resources on this?
There is more information. A recent attempt was made at proving that P is not equal to NP, and it involved trying to avoid relativisations. I was wondering if someone might have more information on this so that I may be able to learn more on the techniques involved. For example, a link to the paper would be good.
Again, any help on this topic would be greatly appreciated.
I found this blog (from Terry Tao) interesting on the subject.
Related
Are there any recent (feel free to add the "old" ones too) problems that were perceived as NP and then later someone came up with a solution that is Polynomial? I think studying those cases would help in developing a knack of critical problem solving along with practicing competitive programming.
One of such problems is that of deciding whether a given integer is prime. PRIMES IS IN P is the famous paper that broke this news in 2002, to almost everyone's surprise.
I think that you will find this link helpful.
I have been trying to understand Daniel Page's algorithm for
generating restricted weak composition. However, I could not understand it totally. Can someone explain it in more simpler terms? I do not have a theoretical mathematics background.
You can find my paper at http://www.springerlink.com/content/w31081rw26p610t1/?MUD=MP , or my accepted version at http://drpage.pagewizardgames.com/daniel_r_page_GAfRWCG.pdf (please cite the final version, not the accepted version) if you have any questions about the algorithm. This is the paper on that algorithm.
Can somebody please provide a gist of the Byzantine Fault Tolerant algorithm and Liskov's algorithm?
Thanks.
I think the introduction to Chapter 4 of Castro and Liskov's article from 1999 gives a concise and good overview of the inner workings of the algorithm: http://pmg.csail.mit.edu/papers/osdi99.pdf
You can know much details of how PBFT works by reading the paper published in OSDI(1999).
If you want to have understanding the algorithm throughly used in PBFT, then, I highly recommend doctoral thesis and technical paper. Both are written by original author, Miguel Castro. It contains almost everything that you want to know about PBFT. And if you want to see its implementation in code-level, you can download and check the software in this page.
I am planning to implement spam filter using Naive Bayesian classification model.
Online I see a lot of info on Naive Bayesian classification, but the problem is its a lot of mathematical stuff, than clearly stating how its done. And the problem is I am more of a programmer than a mathematician (yes I had learnt Probability and Bayesian theorem back in school, but out of touch for a long long time, and I don't have luxury of learning it now (Have nearly 3 weeks to come-up with a working prototype)).
So if someone can explain or point me to location where its explained for programmers than a mathematician, it would be a great help.
PS: By the way I have to implement it in C, if you want to know. :(
Regards,
Microkernel
The book Programming Collective Intelligence has chapter that covers this and other methods. The chapter (#6) can be understood without reference to previous chapters, is written clearly, and discusses only the minimal mathematics necessary to get the job done.
You could try this website. It's got some source code.
I would highly recommend Andrew Moore's tutorials and I think you should start with this one.
You could also take a look at POPFile, an open source spam filter engine.
Have you looked at dspam?
http://dspam.irontec.com/faq.shtml#1.0
http://www.nuclearelephant.com/
I've got interviews coming up for an internship this summer, and I'd like to review common algorithms and data structures so that I won't be caught off guard by any of the technical questions.
Can anyone recommend a good resource, online or otherwise, for a refresher on common things like shuffling an array, tree traversal, linked lists, etc?
Robert Sedgewick's "Algorithms in $language" are a nice source.
http://www.cs.princeton.edu/~rs/
And of course, Cormen et. al.'s "Introduction to Algorithms" for a more abstract view
http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=11866
Oh, and of course, can't forget Knuth's "The Art of Computer Programming", the definitive compendium...
http://en.wikipedia.org/wiki/The_Art_of_Computer_Programming
This book has a decent review for the basics along with code samples: Programming Interviews Exposed. MIT has an open courseware algorithms class with video lectures here. That goes into way more depth, but you can skip around and pick one what you want. I'm sure just searching google for "algorithms site:.edu" will bring up lots of useful results too.