On (Dynamic) Range Minimum Queries in External Memory

We study the one-dimensional range minimum query (RMQ) problem in the external memory model. We provide the first spaceoptimal solution to the batched static version of the problem. On an instance with N elements and Q queries, our solution takes Θ(sort(N + Q)) = Θ ( N+Q B logM/B N+Q B ) I/O complexity and O(N + Q) space, where M is the size of the main memory and B is the block size. This is a factor of O(logM/B N) improvement in space complexity over the previous solutions. We also show that an instance of the batched dynamic RMQ problem with N updates and Q queries can be solved in O ( N+Q B log2M/B N+Q B ) I/O complexity and O(N +Q) space.