Two Dimensional Range Minimum Queries and Fibonacci Lattices
نویسندگان
چکیده
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 2DRMQs that uses O(N/c) bits additional space with O(c log c(log log c)) 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(c log c) with the same space usage.
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