The nearest object means the path from the initial position to this object is shorter than the path from initial position to any other object. The path is the smallest number of pixels this object must move to reach the target object while making sure that it does not collide with any obstacle.
Like in this example below, consider that object A has to determine which object is closer, object B or object C. The pink rectangle is an obstacle. Now if we consider the euclidean distance, object B will be closer but due to the presence of an obstacle euclidean distance will give false answers.
The ideal solution should give the answer as an object the path to which is no more than 10% larger than to the nearest object. And it should take no more than 10 millisecond on a modestly powered computer to find the nearest object for 1000 different objects on a map that has upto 1000 obstacles of different sizes and the map is no larger than 1000*1000 pixels (like in the image above the nearest object for A is C, for B it is A and for C it is A). Also it should not take more than 50 MB of RAM (excluding the size of RAM used to store the coordinates of objects and obstacles and their sizes).
And the map is dynamic. The solution need not return the path between the objects, it need to only find the nearest object.
What will be the ideal solution of this problem?