Abstract
Given a matrix of size N, two dimensional range minimum queries (2D-RMQs) ask for the position of the minimum element in a rectangular range within the matrix. We study trade-offs between the query time and the additional space used by indexing data structures that support 2D-RMQs. Using a novel technique—the discrepancy properties of Fibonacci lattices—we give an indexing data structure for 2D-RMQs that uses O(N/c) bits additional space with O(clogc(loglogc)2) query time, for any parameter c, 4 ≤ c ≤ N. Also, when the entries of the input matrix are from {0,1}, we show that the query time can be improved to O(clogc) with the same space usage.
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Brodal, G.S., Davoodi, P., Lewenstein, M., Raman, R., Srinivasa Rao, S. (2012). Two Dimensional Range Minimum Queries and Fibonacci Lattices. In: Epstein, L., Ferragina, P. (eds) Algorithms – ESA 2012. ESA 2012. Lecture Notes in Computer Science, vol 7501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33090-2_20
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DOI: https://doi.org/10.1007/978-3-642-33090-2_20
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