Combined Data Structure for Previous-And Next-Smaller-Values

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Executive Summary

The authors consider the situation where a static array A[1, n] can be preprocessed such that the following three queries can be answered in constant time: previous- and next-smaller-value-queries, where given a position i in A, one searches for the next position p to the left (or right) of i with A[p] < A[i], and range minimum queries, where for two given indices i and j they look for the position of the minimum element within the sub-array A[i..j].

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