data structures – Can an algorithm complexity be lower than its tight low bound / higher than its tight high bound?

Let $t(x)$ be the time taken for input $xin {0,1}^*$, and $T(n)=max_{xin{0,1}^*,|x|=n}t(x)$ is the worst case.

If $Tintheta(n^3log(n))$, this means that there are constants $C_1,C_2$ and $N$ such that for all $n> N$ you have $$C_1n^3log(n)leq T(n)leq C_2n^3log(n)$$.

Since $n^3log(n)geq n^2$ for $n>1$, then $C_1n^2leq C_1n^3log(n)leq T(n)$. Therefore, $TinOmega(n^2)$.

We also have that $n^3log(n)leq n^4$, for all $n>1$. Therefore, $T(n)leq C_2n^3log(n)leq C_2n^4$.

This implies that $Tin O(n^4)$.

Finally, $$begin{align}A(n)&=E(t(x), |x|=n)\&leq E(T(n), |x|=n)\&=T(n)E(1,|x|=n)\&=T(n)\&leq C_2n^3log(n)\&leq C_2n^4end{align}$$, for $n>1$. Therefore, the average number of steps satisfies $Ain O(n^4)$.


Sometimes computing tight bounds is hard, while more relaxed bounds are more accessible.

video – FFmpeg not able to record screen at high fps

I have been trying to record a video playing on chrome on my desktop (1920 * 1080) at 60 fps using ffmpeg. Not very familiar with ffmpeg so please correct me if I wrote something incorrect in the post. Below are my system specs:-

Windows 10

Ryzen 3600

16 GB RAM

Nvidia GTX 1650

240GB SSD

The command that I am running is-

ffmpeg -thread_queue_size 5096 -f gdigrab -framerate 60 -probesize 42M -s 1920x1080 -rtbufsize 2000M -i desktop -c:v h264_nvenc -preset llhp output.mkv

But the final output stutters and is recorded at around 21-23 fps (Can see this from the ffmpeg output). I checked my task manager and nothing seems to be maxing out.

I am pasting the ffmpeg log output below

ffmpeg version git-2020-06-28-4cfcfb3 Copyright (c) 2000-2020 the FFmpeg developers
  built with gcc 9.3.1 (GCC) 20200621
  configuration: --enable-gpl --enable-version3 --enable-sdl2 --enable-fontconfig --enable-gnutls --enable-iconv --enable-libass --enable-libdav1d --enable-libbluray --enable-libfreetype --enable-libmp3lame --enable-libopencore-amrnb --enable-libopencore-amrwb --enable-libopenjpeg --enable-libopus --enable-libshine --enable-libsnappy --enable-libsoxr --enable-libsrt --enable-libtheora --enable-libtwolame --enable-libvpx --enable-libwavpack --enable-libwebp --enable-libx264 --enable-libx265 --enable-libxml2 --enable-libzimg --enable-lzma --enable-zlib --enable-gmp --enable-libvidstab --enable-libvmaf --enable-libvorbis --enable-libvo-amrwbenc --enable-libmysofa --enable-libspeex --enable-libxvid --enable-libaom --enable-libgsm --disable-w32threads --enable-libmfx --enable-ffnvcodec --enable-cuda-llvm --enable-cuvid --enable-d3d11va --enable-nvenc --enable-nvdec --enable-dxva2 --enable-avisynth --enable-libopenmpt --enable-amf
  libavutil      56. 55.100 / 56. 55.100
  libavcodec     58. 93.100 / 58. 93.100
  libavformat    58. 47.100 / 58. 47.100
  libavdevice    58. 11.100 / 58. 11.100
  libavfilter     7. 86.100 /  7. 86.100
  libswscale      5.  8.100 /  5.  8.100
  libswresample   3.  8.100 /  3.  8.100
  libpostproc    55.  8.100 / 55.  8.100
(gdigrab @ 000002289415e2c0) Capturing whole desktop as 1920x1080x32 at (0,0)
Input #0, gdigrab, from 'desktop':
  Duration: N/A, start: 1594273685.053229, bitrate: 3981337 kb/s
    Stream #0:0: Video: bmp, bgra, 1920x1080, 3981337 kb/s, 60 fps, 1000k tbr, 1000k tbn, 1000k tbc
Stream mapping:
  Stream #0:0 -> #0:0 (bmp (native) -> h264 (h264_nvenc))
Press (q) to stop, (?) for help
Output #0, matroska, to 'output.mkv':
  Metadata:
    encoder         : Lavf58.47.100
    Stream #0:0: Video: h264 (h264_nvenc) (Main) (H264 / 0x34363248), rgb0, 1920x1080, q=-1--1, 2000 kb/s, 60 fps, 1k tbn, 60 tbc
    Metadata:
      encoder         : Lavc58.93.100 h264_nvenc
    Side data:
      cpb: bitrate max/min/avg: 0/0/2000000 buffer size: 4000000 vbv_delay: N/A
frame=  600 fps= 23 q=25.0 Lsize=    1533kB time=00:00:26.21 bitrate= 478.9kbits/s speed=   1x
video:1528kB audio:0kB subtitle:0kB other streams:0kB global headers:0kB muxing overhead: 0.311876%
Exiting normally, received signal 2. 

In the last, you can see the fps=23 mark. I am not sure why I am not able to record it at the specified fps. The video which I record appears choppy because of this.

But if I do the same recording using OBS, it seems to work fine. Not exactly sure what different is happening there. But I need to do it through the ffmpeg command line only. Please guide. Thanks!

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High CPU load on EC2 with Nginx/Celery/Django causes server to fail

I am running a Django web app on an EC2 server using Nginx, and uWSGI. I also have Celery running some background tasks (no CRON jobs, just on occasional user actions).

The app is in early closed Beta with no users currently active.

Over the past three days, the server would fall over after experiencing super high CPU loads, seemingly randomly (see screengrab).

Before this, the app was running without issue for weeks. I made some programmatic changes to the website, but not to the server configuration (consolidating models mostly).

I tried to pick something up from the logs (Nginx access.log, error.log and Django debug.log), but I don’t see any errors or oddities (don’t have access to the logs right now).

In addition, I experienced a similar effect when migrating model changes (in venv) if I haven’t restarted the server beforehand. Sometimes, even when restarting the server, it would become so slow I would have to wait several minutes for Celery to restart.

I need help to find a starting point to investigate the problem. Any ideas?

Server Load

ubuntu mate – High computer case temperature

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I put a thermometer in and it read around 100 degrees F.

After the process, the temp went to around 80 degrees.

Do I need to be concerned?

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