## Algorithms: Smooth requests to rate the API limited

``````        wasted requests     not enough time for those requests
|                       |
|                       |
(1) |-x--x-----------------x----x--x--x| x  x   (executing requests)
..                   .    .....           (sending requests)
(2) |-x--x-----------------x----xxxx-x-|        (executing requests)

(3) |xx-x--x--x---x---x----x----x-----x|        (executing requests, ideal)
``````

I am trying to find out when to send requests to an API that will be spaced as consistently as possible.

The most direct solution would be to keep the requests sufficiently spaced so that the API does not accelerate (1). However, this technique wastes many requests.

I came up with the idea of ​​letting requests run much faster when there is a lot of space left and reducing speed when at the end (3). However, when the API after the interval received its 120th request at the last minute, the requests were too slow. It would be optimal to send every 0.5 seconds (60/120), but my script sent them every 0.85 seconds.

How would you achieve something similar to the example shown in (2)?

## c ++ – DirectX: MFC OnIdle limited to 60 fps

I have a very particular problem …

I have directx classes to render in a window. I have created a GUI with MFC c ++ and I have integrated my DirectX classes with it. I am initializing in the OnInitDialog function and then making a representation loop in the OnIdle function. I have mounted the WindowProc function. It is a model dialogue.

The problem is that, regardless of the VSYNC state of my directx component (I know the current indicators of the exchange chain by the way), I always get a frame rate of 60 fps. When I minimize the window, the frame rate is unlocked and becomes very high. When maximizing again, it falls back to 60 fps.

An image control is my area of ​​representation, which is a frame.

rendering begins when the user clicks on a button.

So how to unlock frame rate in MFC OnIdle.

## sharepoint online: user permission lock mode with limited access

I talked to MS and they told me that you can disable the limited access user permission blocking mode feature, while the SharePoint Server Publishing Infrastructure feature is active. Ask them to send me an email stating that fact, so if any of that comes up, I have proof that they told me. I'm not sure it will help, but it can't hurt.

## calculation: proof that if f & # 39; is limited at the fixed point, then f & # 39; is limited in some interval

I have a question related to Problem 10 in Exercises 1.7 (p. 35) in the book "Discreet Chaos," Saber Elaydi. The problem is:

"Assume that $$f$$ is continuously differentiable in $$x ^ *$$. Prove that yes $$| f & # 39; (x ^ *) | <1$$, for a fixed point $$x ^ *$$ from $$f$$, then there is an interval $$I = (x ^ * – delta, x ^ * + delta)$$ such that $$| f & # 39; (x) | leq M <1$$ for all $$x in I$$ and for some constant $$M$$. "

My attempt was: $$f$$ is continuously differentiable in $$x ^ *$$, then it is continuous in $$x ^ *$$so for everyone $$epsilon> 0$$ $$exist delta> 0$$
such that $$| x- x ^ * | < delta implies | f (x) – f (x ^ *) | < epsilon$$.

I wanted to show that in the interval $$(x ^ * – delta, x ^ * + delta)$$ holds: $$| f & # 39; (x) | leq M <1$$for some $$M$$.

We can write $$| f & # 39; (x) |$$ how:
$$| f & # 39; (x) | = | f & # 39; (x) – f & # 39; (x ^ *) + f & # 39; (x ^ *) | leq | f & # 39; (x) – f & # 39; (x ^ *) | + | f & # 39; (x ^ *) | leq epsilon + 1$$, where $$x in (x ^ * – delta, x ^ * + delta)$$

Now I don't know what to do, can anyone help me? Thanks in advance.

I am not an administrator here!

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## Algorithms: minimum cut with a balanced and limited number of nodes in each partition: does it have an efficient solution or even a name?

I would like to eliminate the minimum number of edges of an unweighted unaddressed graph to divide the nodes into an arbitrary number of connected components $$S_1$$, $$S_2$$,$$S_3$$$$S_k$$ while maximizing the size (number of nodes) of the smallest partition and with a restriction that limits the size of each partition: $$| S_i | leq c$$ for all $$i$$

Sample Entry: $$c = 30$$; Graph with 40 nodes that are fully connected and 20 nodes that have an edge each
Output example: 30 of the fully connected nodes are placed in $$S_1$$ and everything else (30 nodes) is placed in $$S_2$$.

This is similar to the minimum k cut, but I cannot find a name for this problem with arbitrary k. I can't use a minimum k-cut solver because I would divide the 10 single-edged nodes into 10 sets before I start dividing the 40 fully connected nodes. The closest I could find were the most balanced minimum cuts, but that only deals with a single st cut.

The approximate and probabilistic / random solutions are totally fine for my application if that is what it takes to obtain a decent space / time complexity.

Background story: I am trying to solve a difficult problem with large graphics in which I can only process a small number of input nodes (for example, 30) at a time because the problem is otherwise intractable. If these partitions have many borders for the rest of the graph, the solution will be suboptimal.

Comments on similar problems or providing prior knowledge are also welcome!

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