In this PhD thesis, we deal with binet matrices, an extension of network
matrices. The main result of this thesis is the following. A rational matrix A
of size n times m can be tested for being binet in time O(n^6 m). If A is
binet, our algorithm outputs a nonsingular matrix B and a matrix N such that [B
N] is the node-edge incidence matrix of a bidirected graph (of full row rank)
and A=B^{-1} N.
Furthermore, we provide some results about Camion bases. For a matrix M of
size n times m', we present a new characterization of Camion bases of M,
whenever M is the node-edge incidence matrix of a connected digraph (with one
row removed). Then, a general characterization of Camion bases as well as a
recognition procedure which runs in O(n^2m') are given. An algorithm which
finds a Camion basis is also presented. For totally unimodular matrices, it is
proven to run in time O((nm)^2) where m=m'-n.
The last result concerns specific network matrices. We give a
characterization of nonnegative {r,s}-noncorelated network matrices, where r
and s are two given row indexes. It also results a polynomial recognition
algorithm for these matrices.Comment: 183 page
