Lower bounds for external algebraic decision trees

We propose a natural extension of algebraic decision trees to the external-memory setting, where the cost of disk operations overwhelms CPU time, and prove a tight lower bound of Ω(n log _m n) on the complexity of both sorting and element uniqueness in this model of computation. We also prove a Ω(min{n log _mn, N}) lower bound for both problems in a less restrictive model, which requires only that the worst-case internal-memory computation time is finite. Standard reductions immediately generalize these lower bounds to a large number of fundamental computational geometry problems.