Solve a floor planning problem given graphs H & V

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% Section 8.8.1/2, Example 8.7, Boyd & Vandenberghe "Convex Optimization"
% Joelle Skaf - 11/13/05
% (a figure is generated)
%
% Rectangles aligned with the axes need to be place in the smallest
% possible bounding box. No overlap is allowed. Each rectangle to be placed
% can be reconfigured, within some limits.
% In the current problem, 5 rectangles are to be place. We are given 2
% acyclic graphs H and V (for horizontal and vertical) that specify the
% relative positioning constraints of those rectangles.
% We are also given minimal areas for the rectangles.

% Input data
n = 5;
% for each entry i, X_tree(i) = parent(i)
H_tree = [0 0 1 0 0;...
          0 0 1 0 0;...
          0 0 0 0 1;...
          0 0 0 0 1;...
          0 0 0 0 0];
V_tree = [0 0 0 1 0;...
          1 0 0 0 0;...
          0 0 0 1 0;...
          0 0 0 0 0;...
          0 0 0 0 0];

Amin = [100 100 100 100 100; ...
         20  50  80 150 200; ...
        180  80  80  80  80; ...
         20 150  20 200 110];
rho = 1;          % minimum spacing constraints

% solving the problem by calling the general FLOORPLAN routine
for iter = 1:4
    A = Amin(iter,:);
    [W, H, w, h, x, y] = floorplan(H_tree, V_tree, rho, A, 1/5*ones(n,1), 5*ones(n,1));
    % Plotting
    subplot(2,2,iter)
    for i=1:n
        fill([x(i); x(i)+w(i); x(i)+w(i); x(i)],[y(i);y(i);y(i)+h(i);y(i)+h(i)],0.90*[1 1 1]);
        hold on;
        text(x(i)+w(i)/2, y(i)+h(i)/2,['B',int2str(i)]);
    end
    axis([0 W 0 H]);
    axis equal; axis off;
end