Permuting and Batched Geometric Lower Bounds in the I/O Model

We study permuting and batched orthogonal geometric reporting problems in the External Memory Model (EM), assuming indivisibility of the input records. Our main results are twofold. First, we prove a general simulation result that essentially shows that any permutation algorithm (resp. duplicate removal algorithm) that does αN/B I/Os (resp. to remove a fraction of the existing duplicates) can be simulated with an algorithm that does α phases where each phase reads and writes each element once, but using a factor α smaller block size. Second, we prove two lower bounds for batched rectangle stabbing and batched orthogonal range reporting queries. Assuming a short cache, we prove very high lower bounds that currently are not possible with the existing techniques under the tall cache assumption. 1998 ACM Subject Classification F.2.2. Nonnumerical Algorithms and Problems, G.2.1. Combinatorics