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I think your diagram is wrong, since it assumes that undecidable problems are always semi-decidable. Some semi-decidable problems are undecidable (like the Halting Problem) and all decidable problems are semi-decidable.
That depends on the network capacity, protocols involved etc. I suggest you look into some Computer Network books like Fourozan or Kurose-Ross. Please accept the answer if it has answered your original question.
Start with completely unsorted strings of length 4 and work upto 10. Observe if there are any patterns between the number of recursion tree levels and the number of characters in the string. Extend this pattern for strings of 11 characters. You will get a general formula.
A frame contains a packet. So once we isolate a frame, the frame contains the header and the data part. Simply stripping the header of the frame gives us the payload/data of the frame. This payload is nothing but the packet / datagram / network layer unit.
Note that everything I described is just an example. The stop and start sequences were chosen as same and chosen randomly. It depends on the underlying protocol used the Network stack. These are called frame delimiters. Look it up.
Try looking up Segment Trees and Fenwick Trees. These definitely have to be altered to fit your particular model. Range Minimum Query Data Structures were exclusively developed to help model such questions.
+1. I refrained from mentioning them and went for implementations because I remember my professors mentioning them with a footnote that Voronoi Diagrams are computationally quite complex to implement in higher dimensions. So simple kNN implementations get the job done much better. However the condition that "lines are drawn to be equidistant between two points" may not be fulfilled.
