Years and Authors of Summarized Original Work
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2011; Fischer, Heun
Problem Definition
Given a static array A of n totally ordered objects, the range minimum query problem (RMQ problem) is to build a data structure \(\mathcal{D}\) on A that allows us to answer efficiently subsequent online queries of the form “what is the position of a minimum element in the subarray ranging from i to j?” (We consider the minimum; all results hold for maximum as well.) Such queries are denoted by RMQ A (i, j) and are formally defined by \(\text{RMQ}_{A}(i,j) =\mathrm{ argmin}_{i\leq k\leq j}{\bigl \{A[k]\bigr \}}\) for an array A[1, n] and indices 1 ≤ i ≤ j ≤ n. In the succinct or compressed setting, the goal is to use as few bits as possible for \(\mathcal{D}\), hopefully sublinear in the space needed for storing A itself. The space for A is denoted by | A | and is \(\vert A\vert =\varTheta (n\log n)\) bits if A stores numbers from a universe of size \(n^{\varTheta (1)}\).
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Fischer, J. (2016). Compressed Range Minimum Queries. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_640
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