Finding local maxima in a 2D array

Question

A local maximum in a 2D array can be defined as a value such that all it\'s 4 neighbours are less than or equal to it, ie, for a[i][j] to be a local maximum,

Answer 1

I am pretty sure this cannot be solved in less than O(n^2) comparisons. Assume a chess board 2d matrix where all the white squares are 1 and blacks are 0. It wiil will have O(n^2) solutions and each solution requires at least one comparison.