Applications of matroids in electric network theory

Abstract

Professor Masao Iri and his students had several important contributions to the theory of electric networks. He was one of the first scientists who recognized the importance of matroid theory in studying the qualitative problems of electric networks. The present paper summarizes his results in the unique solvability of linear active networks and in the existence of hybrid immittance description of linear multiports. Then his contribution to the proper understanding of the duality principle in electric network theory is presented. The last two sections are strongly related to the concept of genericity, leading to some results in the qualitatively reliable synthesis of linear multiports and to some considerations on how to store the data of linear multiports. These applications require a broad spectrum of matroidal tools, like the matroid partition, intersection and parity algorithms and concepts like matroid union, gammoids, transversal matroids, etc. The survey is extended by some more recent results showing that the influence of Professor Iri to the younger generation of researchers will be thriving for many years to come.