Lower bounds for data structure problems on RAMs

A technique is described for deriving lower bounds and tradeoffs for data structure problems. Two quantities are defined. The output variability depends only on the model of computation. It characterizes in some sense the power of a model. The problem variability depends only on the problem under consideration. It characterizes in some sense the difficulty of the problem. The first theorem states that if a model's output variability is smaller than the problem variability, a lower bound on the worst case (average case) time for the problem follows. A RAM that can add, subtract and compare unbounded integers is considered. The second theorem gives an upper bound on the output variability of this model. The two theorems are used to derive lower bounds for the union-find problem in this RAM.<>