Optimization with binet matrices

Abstract

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