That's good because then when we run imagine that we have some kind of satisfiability algorithm that runs in polynomial time it's running on a polynomial size input, so it's not like we're running a polynomial time algorithm on an exponential size input, which would take exponential time to run.

like the degree polynomial to use with the learning algorithm or choose the regularization parameter for learning algorithm.

Time estimation algorithm

linear time top K algorithm.

We eventually determine the running time of the algorithm.

Let's say this is my polynomial, let me call my polynomial p of x.

NP hard and therefore a polynomial time solution for that problem solves everything in NP.

Algorithm to estimate the time when a torrent is finished

Here's the gradient descent algorithm that we saw last time.

And that is lead theoreticians at least to find efficient in one particular way sometimes and that is that an algorithm is efficient if it has a polynomial bound on its running time.

Algorithm

learning algorithm A or learning algorithm

The algorithm is a recursive algorithm.

So there has to be some kind of polynomial upper bound of an algorithm to solve that problem for the problem to be in p.

Having completed our first analysis of an algorithm, namely an upper bound on the running time of the Merge Short algorithm.

Other words, what is the running time of the merge sort algorithm?

Noise algorithm

Scaling Algorithm

Expansion algorithm

Slider algorithm

Synergistic algorithm

Signature Algorithm

Authentication algorithm

Dither Algorithm

Dithering Algorithm

Cipher algorithm

Hash algorithm

Digest algorithm

Formerly the class NP is the set of non deterministic polynomial time decidable problems that is to say that it's a problem that can be dissolved by a program that runs in polynomial time that has non deterministic elements in it.

First, it has to be NP hard, meaning that nothing in NP is harder then X. Which is to say that if you could solve X in polynomial time, you could use it to solve everything in NP in polynomial time.

We know that every problem that's in P is in NP and every problem that is NP is in EXP, that is to say any problem that you can solve in polynomial time, we can certainly solve in non deterministic polynomial time, and any problem that we can solve in a non deterministic polynomial time, we can also solve in exponential time, but here's what we don't know.

Suppose you like to decide what degree of polynomial to fit to a data set, sort of what features to include to give you a learning algorithm.

I have this polynomial in the denominator here.

That problems that are in NP don't necessarily require exponential time, but they may not be solvable in polynomial time either we don't know.

low order polynomial such as a plus one, when we really needed a higher order polynomial to fit the data.

What does that give us for a running time for this entire algorithm?

So it's as if there's one extra parameter in this algorithm, which I'm going to denote d, which is what degree of polynomial do you want to pick?

All right, so now we're in a good position to define the set p of polynomial time decidable problems.

Sometimes a quadratic polynomial, or just a quadratic itself, or quadratic expression, but all it means is a second degree polynomial.

But intuitively, you should think of the running time of an algorithm, you should imagine that you're just running the algorithm in a debugger.

Image compression algorithm

Mapping projection algorithm

Unknown key algorithm

So the constant time algorithm for this problem is just to always say yes.

Then we run an algorithm for solving problem X to get solutions to those and maybe that generates more instances but after polynomial number of calls to this algorithm, what comes spitting out is a solution to the original instance of problem Y.