As part of a solution to an earlier question, I am interested in the following problem.
I have a 2-D matrix $M$. I want to preprocess it in linear time so that I can answer queries of the following form in constant time:
Given $i_1 \leq i_2$ and $j_1 \leq j_2$, what is the minimum of $\{ M_{ij} : i_1 \leq i \leq i_2, j_1 \leq j \leq j_2 \}$?
Such a method is described in On Space Efficient Two Dimensional Range Minimum Data Structures, but I am unable to understand it.
