We define binet matrices, which furnish a direct generalization of totally unimodular network matrices and arise from the node-edge incidence matrices of bidirected graphs in the same way as network matrices do from directed graphs. We develop the necessary theory, give binet representations for interesting sets of matrices, characterize totally unimodular binet matrices and discuss the recognition problem. We also prove that binet constraint matrices guarantee half-integral optimal solutions to linear programs.
This paper deals with linear and integer programming problems in which the constraint matrix is a binet matrix. Binet matrices are pivoted versions of the node-edge incidence matrices of bidirected graphs. It is shown that efficient methods are available to solve such optimization problems. Linear programs can be solved with the generalized network simplex method, while integer programs are converted to a matching problem. It is also proved that an integral binet matrix has strong Chvátal rank 1. An example of binet matrices, namely matrices with at most three non-zeros per row, is given.
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