Is there a tool/algorithm that takes the square room and table

>>58104069
make one

Yes, it's called convex optimization. Here is a free course on it: http://online.stanford.edu/course/convex-optimization-winter-2014

>>58104069
https://www.google.com/search?q=how+to+draw+a+circle

>>58104069
If you're trying to optimize the perimeter of a shape inscribed in a square, you can't do better than a square.

for a circle:
p = pi * d

for a square:
p = 4 * d

So you'll get more room along the walls if you line everybody up against the walls.

Now it's a recursive problem, square within a square again to fit as many people as possible (with the outermost square having their backs to the wall).

Try Gurobi optimisation