Optimal Bounds for the Predecessor Problem

@inproceedings{Beame1999OptimalBF,
  title={Optimal Bounds for the Predecessor Problem},
  author={Paul Beame and Faith Ellen},
  booktitle={STOC},
  year={1999}
}
We obtain matching upper and lower bounds for the amount of time to find the predecessor of a given element among the elements of a fixed efficiently stored set. Our algorithms are for the unit-cost word-level RAM with multiplication and ex tend to give optimal dynamic algorithms. The lower bounds are proved in a much stronger communication game model, but they apply to the cell probe and RAM models and to both static and dynamic predecessor problems. 

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