Galactic algorithm
A galactic algorithm is one that runs faster than any other algorithm for problems that are sufficiently large, but where "sufficiently large" is so big that the algorithm is never used in practice. An example is an algorithm that is the fastest known way to multiply two numbers, provide the numbers have at least 10214857091104455251940635045059417341952 digits.[1] Since this requires (vastly) more digits than there are atoms in the universe, this algorithm is never used in practice. Galactic algorithms were so named by Richard Lipton and Ken Regan[2].
Despite the fact that they will never be used, galactic algorithms may still contribute to computer science:
- An algorithm, even if impractical, may show new techniques that may eventually be used to create practical algorithms.
- Computer sizes may catch up to the crossover point, so the previously impractical algorithm is used.
- An impractical algorithm can still demonstrate that conjectured bounds can be achieved, or alternatively show that conjectured bounds are wrong. As Lipton says "This alone could be important and often is a great reason for finding such algorithms. For an example, if there were tomorrow a discovery that showed there is a factoring algorithm with a huge but provably polynomial time bound that would change our beliefs about factoring. The algorithm might never be used, but would certainly shape the future research into factoring."
References
- ^ David Harvey and Joris Van Der Hoeven. "Integer multiplication in time O(n log n)".
- ^ Lipton, Richard J., and Kenneth W. Regan (2013). "David Johnson: Galactic Algorithms". People, Problems, and Proofs. Heidelberg: Springer Berlin. pp. 109–112.
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