The Randomized Complexity of Maintaining the Minimum

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 ) \Gamma 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, but no deterministic algorithm. Finally, a deterministic algorithm with constant amortized cost per operation for an offline version of the problem is given. 1 Introduction We consider the complexity of maintaining a set S of elements from a totally ordered universe under the following operations: Insert(e): inserts the element e into S, Delete(e): removes from S the element e provided it is known where e is stored, and FindMin: returns the minimum element in S without removing it. We refer to this problem as the Insert-Delete-FindMi..