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000111355 0247_ $$2doi$$a10.5075/epfl-thesis-3938
000111355 02470 $$2urn$$aurn:nbn:ch:bel-epfl-thesis3938-4
000111355 02471 $$2nebis$$a5419910
000111355 037__ $$aTHESIS 000111355 041__$$aeng
000111355 088__ $$a3938 000111355 245__$$aRecognition of generalized network matrices
000111355 269__ $$a2007 000111355 260__$$bEPFL$$c2007$$aLausanne
000111355 300__ $$a183 000111355 336__$$aTheses
000111355 502__ $$aDominique de Werra, Jean Fonlupt, Michele Conforti 000111355 520__$$aIn 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.
000111355 6531_ $$anetwork matrices 000111355 6531_$$abinet matrices and Camion bases
000111355 6531_ $$amatrices réseau 000111355 6531_$$amatrices binet and bases de Camion.
000111355 700__ $$0(EPFLAUTH)167950$$g167950$$aMusitelli, Antoine 000111355 720_2$$aLiebling, Thomas M.$$edir.$$g105665$$0241744 000111355 720_2$$aFukuda, Komei$$edir.$$g107359$$0240750 000111355 8564_$$zTexte intégral / Full text$$yTexte intégral / Full text$$uhttps://infoscience.epfl.ch/record/111355/files/EPFL_TH3938.pdf$$s1635392 000111355 909C0$$pROSO$$0252055 000111355 909CO$$pthesis$$pthesis-bn2018$$pDOI$$ooai:infoscience.tind.io:111355$$qDOI2$$qGLOBAL_SET 000111355 918__$$dEDMA$$bSB-SMA$$cIMA$$aSB 000111355 919__$$aROSO
000111355 920__ $$b2007$$a2007-10-26
000111355 970__ $$a3938/THESES 000111355 973__$$sPUBLISHED$$aEPFL 000111355 980__$$aTHESIS