Don't Rush into a Union: Take Time to Find Your Roots

@inproceedings{Patrascu2011DontRI,
  title={Don't Rush into a Union: Take Time to Find Your Roots},
  author={Mihai Patrascu and Mikkel Thorup},
  booktitle={STOC},
  year={2011}
}
We present a new threshold phenomenon in data structure lower bounds where slightly reduced update times lead to exploding query times. Consider incremental connectivity, letting t<sub>u</sub> be the time to insert an edge and t<sub>q</sub> be the query time. For t<sub>u</sub> = Omega(t<sub>q</sub>), the problem is equivalent to the well-understood union-find problem: proc{InsertEdge}(s,t) can be implemented by Union(Find(s), Find(t)). This gives worst-case time t<sub>u</sub> = t<sub>q</sub… CONTINUE READING
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