How to construct (0,1)-matrices with prescribed row and column sum vectors
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- All matrix elements are either 1 or 0.
- Both row sum vector and column sum vector are given.
- Return a 3-dimensional result that stacks all possible solutions along the third dimension. (exhaustive, all possible solutions need to be included.)
- Avoid looping at best due to performance, use matrix operations whenever possible.
- Thank you so much for your assistance :)
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Ameer Hamza
2020년 9월 16일
편집: Ameer Hamza
2020년 9월 16일
If rows represent objects, then does that mean that row sum for all values is 1? And the column sum should add up to the number of objects. For example, if there are 200 objects and 20 destinations, then do you have
row_sum = ones(200, 1);
col_sum = % [1x20] matrix where sum(col_sum)=200
Is this correct?
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Ameer Hamza
2020년 9월 16일
Since you are minimizing the dot product, the thing to realize is that this is an integer linear programming problem. Following code apply intlinprog() function.
rng(0);
M = rand(1000, 20); % distance matrix
[m, n] = size(M);
row_sum = ones(m, 1);
col_sum = [50 45 60 35 25 90 30 35 75 90 10 5 30 40 90 60 40 60 45 85];
f = reshape(M', 1, []);
x = repmat({ones(1, n)}, m, 1);
Aeq = [blkdiag(x{:}); repmat(eye(n), 1, m)];
Beq = [row_sum(:); col_sum(:)];
lb = zeros(m*n, 1);
ub = ones(m*n, 1);
sol = intlinprog(f, 1:numel(x0), [], [], Aeq, Beq, lb, ub);
sol = reshape(sol, n, []).';
If you have knowledge about integer linear programming, then the logic of this code is quite easy to follow. Let me know if there is some confusion.
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