Includes bibliographical references (pages 629-643) and index.
Contents
Chapter 1. Introduction -- Chapter 2. Mathematical Preliminaries -- Chapter 3. Graphs -- Chapter 4. Matroids -- Chapter 5. Electrical Networks -- Chapter 6. Topological Hybrid Analysis -- Chapter 7. The Implicit Duality Theorem and Its Applications -- Chapter 8. Multiport Decomposition -- Chapter 9. Submodular Functions -- Chapter 10. Convolution of Submodular Functions -- Chapter 11. Matroid Union -- Chapter 12. Dilworth Truncation of Submodular Functions -- Chapter 13. Algorithms for the PLP of a Submodular Function -- Chapter 14. The Hybrid Rank Problem.
Summary
There is a strong case for electrical network topologists and submodular function theorists being aware of each other's fields. Presenting a topological approach to electrical network theory, this book demonstrates the strong links that exist between submodular functions and electrical networks. The book contains: & bull; a detailed discussion of graphs, matroids, vector spaces and the algebra of generalized minors, relevant to network analysis (particularly to the construction of efficient circuit simulators) & bull; a detailed discussion of submodular function theory in its own right.
