Optimal Succinctness for Range Minimum Queries

For a static array A of n totally ordered objects, a range minimum query asks for the position of the minimum between two specified array indices. We show how to preprocess A into a scheme of size 2n + o(n) bits that allows to answer range minimum queries on A in constant time. This space is asymptotically optimal in the important setting where access to A is not permitted after the preprocessing step. Our scheme can be computed in linear time, using only n + o(n) additional bits for construction. We also improve on LCA-computation in BPSor DFUDS-encoded trees.