Applications of Matroid Theory

M. Iri
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M. Iri: University of Tokyo, Faculty of Engineering, Dept. of Mathematical Engineering

A chapter in Mathematical Programming The State of the Art, 1983, pp 158-201 from Springer

Abstract: Abstract It will be shown that looking at a problem from the viewpoint of matroids enables us to understand the essence of the problem as well as its relations to other problems, clearly, preventing us from probable confusion into which we might have been involved without matroids, and that mathematical techniques developed in matroid theory are powerful for manipulating and solving the mathematical model which would otherwise have been impossible, or at best prohibitively complicated. Examples of problems to be discussed: 1. Topological, geometrical and physical matroids, or faithful and unfaithful representations in terms of matroids 2. Elements and their interconnections 3. Minimum-size systems of equations 4. Structural solvability of systems of equations 5. Two kinds of dualities

Keywords: Constitutive Equation; Bipartite Graph; Electric Network; Elastic Structure; Submodular Function (search for similar items in EconPapers)
Date: 1983
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-68874-4_8

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DOI: 10.1007/978-3-642-68874-4_8

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