Monge array

In computer science, an m-by-n array of real numbers is a Monge array if for all i, j, k, l such that:

and

one obtains:

So whenever we pick two rows and two columns of a Monge array and consider the four elements at the intersection points, the sum of the upper-left and lower right elements is less than or equal to the sum of the lower-left and upper-right elements.

This array is a Monge array:

For example, take the intersection of rows 2 and 4 with columns 1 and 5. The four elements are:

$$

\\begin{bmatrix} 17 & 23\\\\ 11 & 7 \\end{bmatrix}

17 + 7 = 24
23 + 11 = 34

It holds that the sum of the upper-left and lower right elements is less than or equal to the sum of the lower-left and upper-right elements.

Monge arrays are useful for keeping growth of functions in O(nlog n) time or less.

See also:

• quasi-convex