5 research outputs found
Recognition of generalized network matrices
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