How to find clip of video belongs to full video?
If the clips both have the same audio track, you can use audio fingerprinting techniques to identify them. Apart from that, OpenCV can do similarity checks on video: http://docs.opencv.org/2.4/doc/tutorials/highgui/video-input-psnr-ssim/video-input-psnr-ssim.html

And BTW. if using the audio fingerprinting method, as you can see with Shazam or musicbrainz.org seems to be managable from the amount of data.