A scheme’s running time is: O((1/E)^2*n^2). Is this a fully polynomial-time approximation scheme? Explain why?
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A scheme’s running time is: O((1/E)^2*n^2). Is this a fully polynomial-time approximation scheme? Explain why?
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I reading about zero knowledge proofs. In this regard, I have read about zk-SNARKs from the blog by Vitalik Buterin. I understood Flattening, R1CS and QAP polynomials which create proof.
However, I am not able to map what exactly is happening in the proof using polynomials. I mean I know zero knowledge proof has a prover, verifier and witness. There are prover and verifier functions. In the polynomial example explained in the blog, I don't understand what prover and verifier computes. What does the prover compute to prove his legitimacy ?
Anyhelp would be appreciated. Thank you.
Can someone provide a derivation of the equation he gets on 1:15 using quotient rule https://www.youtube.com/watch?v=aVId8KMsdUU&index=18&list=LL2gry7n2BsijUeah-oFnPSg
Pretty simple question, but I get another equation, so I'm stuck.
Thanks in advance.
Your question probably belongs on math.stackexchange.com though.
I am recursively building a graph in java using the graphstream library.. however this graph is so huge so that the recursion is very deep and this ends in stackoverflow. Believe me, even an iteration wouldn't solve my problem.. I will just get a runtime error down the road.
My goal is to use a search algorithm such as Disjktra or A* or whatsoever on the graph in the end.
As I dont have the whole graph, I have been looking in the literature for things such as a shortest path algorithm in a partial maps; use of heuristics I couldn't find much.
I would appreciate it if someone could give me some hints (papers, ideas; an implementation would be a jackpot!!!! :-D) I have looked at algorithms such as PHA* or some others..
I know this post is very old... But I solved it back then using a 1990 Algorithm, from Korf, R. E. (1990) "Real-time heuristic search" Can be found here: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.137.1955&rep=rep1&type=pdf
I can't really seem to grasp what it really means to say a problem is NP-Complete. Could anyone help me with the following question?
An NP-complete problem is a problem for which one can prove that an algorithm for solving it in polynomial time does not exist. Is the statement true?
I would want to say this statement isn't true, because can anyone actually prove that such an algorithm doesn't exist for any NP-Complete problem? From looking around on various sources, I understand that no polynomial time algorithm is known for any NP-Complete problem; however, it can't be proven.
Any help would be greatly appreciated. Thanks.
It is possible in some situations to prove that no algorithm exists that is better than a certain limit.
For example the O(n log n) bound for a comparison sort has been proven. No matter how clever we become in the future, we can be sure that no-one will ever invent an O(n) comparison sort.
In this case though, no-one has found a proof. But that doesn't mean it can't be proven.
The statement is more fundamentally wrong: There are problems that cannot be solved in polynomial time which are much harder than NP problems. The point of NP completeness is a polynomial time solution existing is equivalent to P=NP (which means additionally that a solution not existing means P!=NP).
Can anybody suggest a good book/paper/website/background reading about universal codes for integers and especially Fibonacci code (in the sense of http://en.wikipedia.org/wiki/Fibonacci_code)? Thanks!
Edit: Thanks for the answers and the useful links so far! I am sorry if I have not made myself completely clear: I am not asking about code (as in writing a program) to generate or compute Fibonacci numbers, but about a particular code (as in encoding, or compressing, data) that makes use of Fibonacci numbers.
One paper found with Google Scholar :
Data compression (DA Lelewer, DS Hirschberg - ACM Computing Surveys (CSUR), 1987)
I'm not so familiar with the subject but the article seems to be pretty decent by a brief looking.
I find MIT's online lectures to be a good resource generally. And they address Fibonacci algorithms in some detail: http://www.catonmat.net/blog/mit-introduction-to-algorithms-part-two/
Relevant segments of the video:
[17:49] Algorithms for computing Fibonacci numbers (FBs).
[19:04] Naive recursive algorithm (exponential time) for computing FBs.
[22:45] Bottom-up algorithm for computing FBs.
[24:25] Naive recursive squaring algorithm for FBs (doesn’t work because of floating point rounding errors).
[27:00] Recursive squaring algorithm for FBs.
Information Theory, Inference, and Learning Algorithms has a chapter on codes. It has a free pdf version, check it out.