A lot of that has already been done. In the web browsing context, when you ask for something and get a 304 Not Modified back because your cached copy is still current, that's basically compressing away the entire content of that object, which may be huge.
Your other idea has been done, too, with "WAN optimization", but it generally isn't helpful for one person, because you already have good caching and proxying going on, even if you don't realize it. That works when multiple people are pulling down the same contents.
Basically, already done.
At this point, if you start going "But what if we also did this...!", you are about 95% likely to start getting into the compression crackpot zone. Information can only be squeezed so hard and once you start proposing other exotic solutions the only explanation that works in response is usually "No, that won't work, but you won't believe me, so, prove it. Implement it and sell it for millions of dollars. Be sure to count all the bytes, not just the ones you like." And generally, that's the end of that.
I am far more likely to believe that you have built a working anti-gravity device, which is at least at the very edge of plausibility under certain not-yet-disproven physical theories, than that you have actually made a huge compression advance, which is effectively mathematically impossible. (Not because compression can't be advanced, but because it's only going to advance incrementally from now on. There's no room left for a breakthrough in the general case.)
Your other idea has been done, too, with "WAN optimization", but it generally isn't helpful for one person, because you already have good caching and proxying going on, even if you don't realize it. That works when multiple people are pulling down the same contents.
Basically, already done.
At this point, if you start going "But what if we also did this...!", you are about 95% likely to start getting into the compression crackpot zone. Information can only be squeezed so hard and once you start proposing other exotic solutions the only explanation that works in response is usually "No, that won't work, but you won't believe me, so, prove it. Implement it and sell it for millions of dollars. Be sure to count all the bytes, not just the ones you like." And generally, that's the end of that.
I am far more likely to believe that you have built a working anti-gravity device, which is at least at the very edge of plausibility under certain not-yet-disproven physical theories, than that you have actually made a huge compression advance, which is effectively mathematically impossible. (Not because compression can't be advanced, but because it's only going to advance incrementally from now on. There's no room left for a breakthrough in the general case.)