Most efficient algorithm to find the biggest square in a two dimension map

Question

I would like to know the different algorithms to find the biggest square in a two dimensions map dotted with obstacles.

An example, where o would be obstacl

Answer 1

So here's one rough approach.

Store the x-y positions of all the obstacles.
For each obstacle O
   find obstacle C that is nearest to it column-wise.
   find obstacle R-top that is nearest to it row-wise from the top.
   find obstacle R-bottom that is nearest to it row-wise from the bottom.
   if (|R-top.y - R-bottom.y| != |O.x - C.x|) continue
   Size of the square = Abs((R-top.y - R-bottom.y) * (O.x - C.x))
Keep track of the sizes and positions to find the largest square

Complexity is roughly O(k^2) where k is the number of obstacles. You could reduce it to O(k * log k) if you use binary search.