# 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