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@lengly, as @csarron mentioned, it's quite straight forward to run the API on any Linux platform since you can build and install the source yourself. The python source scripts for toolkit (mvNCCompiler, mvNCProfiler and mvNCChecker) are also available, so as long as you install the Ubuntu and Python dependencies for the toolkit on Jetson, you can run the full SDK on it.
FYI - You only need the API to offload inferences to the NCS. The toolkit is used to profile, validate and compile neural networks into a binary graph file that the NCS can understand.
I would also like to know Intel's response to this question. Theoretically any platform which supports Ubuntu 16 should be supported for NCS. But I think it is the NCS SDK support which may not be available on all platforms. On the NCS site this is stated as minimum system requirement
x86_64 computer running Ubuntu 16.04 or Raspberry Pi 3 Model B running Stretch desktop or Ubuntu 16.04 VirtualBox instance, USB 2.0 Type-A port (Recommend USB 3.0), 1GB RAM, 4GB free storage space
But earlier I have heard from people who have used NCS on Joule board. So above system requirement is either too constrained, or may be applicable only for the latest SDK which was recently released. Let us see what Intel's official response is. You may also want to check on Nvidia forums
For the API part, I can run it successfully since it's open source. For the SDK part, I guess they can't run for now.