Matrix, Graph, and Matroid

  • Kazuo Murota
Part of the Algorithms and Combinatorics book series (AC, volume 20)


This chapter lays the mathematical foundation for combinatorial methods of systems analysis. Combinatorial properties of numerical matrices can be stated and analyzed with the aid of matroid theory, whereas those of polynomial matrices are formulated in the language of valuated matroids in Chap. 5. Emphasis is laid also on the general decomposition principle based on submodularity, and accordingly the Dulmage–Mendelsohn decomposition, which serves as a fundamental tool for the generic-case analysis of matrices, is presented in a systematic manner.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Mathematical Informatics Graduate School of Information Science and TechnologyUniversity of TokyoTokyoJapan

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