The Randomized Complexity of Maintaining the Minimum

Abstract

The complexity of maintaining a set under the operations Insert, Delete and FindMin is considered. In the comparison model it is shown that any randomized algorithm with expected amortized cost t comparisons per Insert and Delete has expected cost at least n/(e2^2t) − 1 comparisons for FindMin.
If FindMin is replaced by a weaker operation, FindAny, then it is shown that a randomized algorithm with constant expected cost per operation exists; in contrast, it is shown that no deterministic algorithm can have constant cost
per operation. Finally, a deterministic algorithm with constant amortized cost per operation for an offline version of the problem is given.