Abstract
We study the one-dimensional range minimum query (RMQ) problem in the external memory model. We provide the first space-optimal 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(\(N+Q \over B\) log M /B \(N+Q \over B\)) 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(log M /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 (\(N+Q \over B\) \(\log^{2}_{M /B}\) \(N+Q \over B\)) I/O complexity and O(N + Q) space.
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Arge, L., Fischer, J., Sanders, P., Sitchinava, N. (2013). On (Dynamic) Range Minimum Queries in External Memory. In: Dehne, F., Solis-Oba, R., Sack, JR. (eds) Algorithms and Data Structures. WADS 2013. Lecture Notes in Computer Science, vol 8037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40104-6_4
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DOI: https://doi.org/10.1007/978-3-642-40104-6_4
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