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Line 2: In [[mathematics]], a '''balanced matrix''' ''B'' is a 0-1 matrix that does not contain any square submatrix of odd order having row and column sum equal to 2. Balanced matrices are important in [[linear ~~programs~~programming]] such as the [[set partitioning problem]], as they are naturally integer. The result is that the solution to a linear program problem will be integer for these cases, without having to explicitly solve an [[integer linear program]]. 0-1 [[Totally unimodular]] matrices are a subset of balanced matrices, and balanced matrices are a subset of [[perfect matrix\|perfect matrices]], therefore any matrix that is totally unimodular is also balanced, however a balanced matrix may not necessarily be [[totally unimodular]]. The following matrix is a 3 order 2-cycle forbidden submatrix:

Balanced matrix: Difference between revisions