How to construct (0,1)-matrices with prescribed row and column sum vectors
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Yingao Zhang
il 15 Set 2020
Commentato: Yingao Zhang
il 21 Feb 2021
- 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
il 16 Set 2020
Modificato: Ameer Hamza
il 16 Set 2020
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
il 16 Set 2020
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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