Packing soft rectangles
Let R be a rectangle with given area a(R), height h(R) and width w(R), and r(1), r(2),..., r(n) be n soft rectangles, where we mean by a soft rectangle a rectangle r whose area a(r) is prescribed but whose aspect ratio rho(r) is allowed to be changed. In this paper, we consider the problem of packing n soft rectangles r(1), r(2),..., r(n) into R. We prove that, if a(R) >= Sigma(1 <= i <= n) a(r(i)) + 0.10103a(max) and a(max) <= 3(min{h(R), w(R)})(2) hold for a(max) = max(1 <= i <= n) a(r(i)), then these n soft rectangles can be packed inside R so that the apect ratio of each rectangle r(i) is at most 3.
packing rectangle aspect ratio approximation algorithm facility layout floorplan