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 extend 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.

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 compactly stored set. Our algorithms are for the unit-cost word RAM with multiplication and are extended to give dynamic algorithms. The lower bounds are proved for a large class of problems, including both static and dynamic predecessor problems, in a much stronger communication game model, but they apply to the cell probe and RAM models.

We obtain improved lower bounds for a class of static and dynamic data structure problems that includes several problems of searching sorted lists as special cases. These lower bounds nearly match the upper bounds given by recent striking improvements in searching algorithms given by Fredman and Willard's fusion trees [9] and Andersson's search data structure [5]. Thus they show sharp limitations on the running time improvements obtainable using the unit-cost word-level RAM operations that those algorithms employ. 1 Introduction Traditional analysis of problems such as sorting and searching is often schizophrenic in dealing with the operations one is permitted to perform on the input data. In one view, the elements being sorted are seen as abstract objects which may only be compared. In the other view, one is able to perform certain word-level operations, such as indirect addressing using the elements themselves, in algorithms like bucket and radix sorting. Traditionally, the second v...