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An Elegant Pairing Function [pdf]

• sorokod 12y ago
  |R x R| = |R| so the existence of such functions is guaranteed but it is nice to see that some are just a method call away. Does anyone know what pairing function on non negative integers is the most efficient in the number of bits it requires ?
  • Someone 12y ago
    This PDF only handles mapping N x N to N and vice versa, though. For R x R, I would mix the bits of the two numbers [a0 a1 a2 a3...] [b0 b1 b2 b3...] to [a0 b0 a1 b1 a2 b2 a3 b3...] I am not sure that is a computable function for infinite-length bit sequences, though. Maybe none of those mapping functions are?
    • sorokod 12y ago
      Ah yes, I was thinking |N x N| = |N|. So is there a pairing function f: NxN -> N which can be used as compression?