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

here is an approach using recurrence relation :-

isSquare(R,C1,C2) = noObstacle(R,C1,R,C2) && noObstacle(R,C2,R-(C2-C1),C2) && isSquare(R-1,C1,C2-1)

isSquare(R,C1,C2) = square that has bottom side (R,C1) to (R,C2) 

noObstacle(R1,C1,R2,C2) = checks whether there is no obstacle in line segment (R1,C1) to (R2,C2)

Find Max (C2-C1+1) which where isSquare(R,C1,C2) = true  

You can use dynamic programming to solve this problem in polynomial time. Use suitable data structure for searching obstacle.