doi:10.5075/epfl-thesis-3938
urn:urn:nbn:ch:bel-epfl-thesis3938-4
nebis:5419910
eng
Musitelli, Antoine
Recognition of generalized network matrices
Lausanne, EPFL
http://infoscience.epfl.ch/record/111355/files/EPFL_TH3938.pdf
In this 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×m can be tested for being binet in time O(n6m). 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-1N. Furthermore, we provide some results about Camion bases. For a matrix M of size n × 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(n2m') 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 {ε, ρ}-noncorelated network matrices, where ε and ρ are two given row indexes. It also results a polynomial recognition algorithm for these matrices.
2007-09-03T12:13:51Z
http://infoscience.epfl.ch/record/111355
http://infoscience.epfl.ch/record/111355
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