A simple linear-space data structure for constant-time range minimum query

Abstract

We revisit the range minimum query problem and present a new O(n)-space data structure that supports range minimum queries in O(1) time. The goal is to construct a static data structure that efficiently supports range minimum queries on a given list A[0:n−1] of n items drawn from a totally ordered set. Each range minimum query consists of an input pair of indices (i,j) for which the minimum element of the subarray A[i:j] must be returned. Although previous data structures exist whose asymptotic bounds match ours, our goal is to introduce a new solution that is simple, intuitive, and practical without increasing asymptotic costs for query time or space. We analyze our new data structure theoretically and practically, the latter through an evaluation of its performance relative to implementations of four of the top range minimum query data structures.