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Nov 17, 2010 at 20:53 comment added Guilherme D. da Fonseca I don't think the question is about a simple and practical algorithm with complex analysis. I think the question is about a simple and practical algorithm with complex running time, that is, the actual expression obtained for the upper bound.
Nov 17, 2010 at 16:15 comment added Neel Krishnaswami The ratio of algorithm length to proof complexity for union-find is probably unbeatable -- all three operations are what, nine lines of code?
Nov 17, 2010 at 8:26 comment added Jukka Suomela Well, $O(\alpha(n))$ time doesn't look that "complicated" if you compare it to $O(n^{4/3} \alpha(n) \log^2 n / \log \log n)$ in Guilherme's answer. :)
Nov 16, 2010 at 23:58 comment added Warren Schudy Indeed, I posted the same answer but deleted it after I noticed you beat me to it. :) Simple and elegant algorithm that a non-theorist might even discover, but inverse Ackermann amortized complexity.
Nov 16, 2010 at 23:43 history answered Kevin Wortman CC BY-SA 2.5