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Net theory and its applications : flows in networks /
Electrical, communication, transportation, computer, and neural networks are special kinds of nets. Designing these networks demands sophisticated mathematical models for their analysis. This book is the first to present a unified, comprehensive, and up-to-date treatment of net theory. It brings tog...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
Imperial College Press,
2003.
|
| Colección: | Series in electrical and computer engineering ;
vol. 1. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1. Graphs and networks. 1.1. Basic definitions of abstract graphs. 1.2. Operations on graphs. 1.3. Nonseparable graphs and bipartite graphs. 1.4. Planar graphs. 1.5. Dual graphs. 1.6. 2-isomorphism. 1.7. Matrices associated with a graph. 1.8. Directed graphs. 1.9. The circuit matrix associated with a planar graph or directed graph. 1.10. Summary and suggested reading
- 2. The shortest directed path problem. 2.1. Shortest directed paths. 2.2. Shortest directed path algorithms. 2.3. Multiterminal shortest directed paths. 2.4. Enumeration of the shortest directed paths by decomposition. 2.5. Summary and suggested reading
- 3. Maximum flows in networks. 3.1. Flows. 3.2. s-t cuts. 3.3. Maximum flow. 3.4. Ford-Fulkerson algorithm. 3.5. Layered nets. 3.6. A blocking flow algorithm. 3.7. Variants of the Ford-Fulkerson algorithm. 3.8. Karzanov algorithm. 3.9. Flows in undirected and mixed nets. 3.10. Flows in node-and-arc capacitated nets. 3.11. Summary and suggested reading
- 4. Minimum trees and communication nets. 4.1. Forests, subtrees and trees. 4.2. Minimum and maximum trees. 4.3. Minimum and maximum tree algorithms. 4.4. Terminal capacity matrix. 4.5. Synthesis of a flow-equivalent tree. 4.6. Synthesis of optimum undirected communication nets. 4.7. Oriented communication nets. 4.8. Summary and suggested reading
- 5. Feasibility theorems and their applications. 5.1. A supply-demand theorem. 5.2. An extended supply-demand theorem. 5.3. Circulation theorem. 5.4. Feasible circulation algorithm. 5.5. Flows in nets with lower bounds on arcs. 5.6. Feasible flows in node-and-arc capacitated nets. 5.7. Summary and suggested reading
- 6. Applications of flow theorems to subgraph problems. 6.1. The subgraph problem of a directed graph. 6.2. Digraphic sequences. 6.3. The subgraph problem of a graph. 6.4. Graphical sequences. 6.5. The (p, s)-matrix. 6.6. Realization of the 1-matrix and the (1, 0)-matrix. 6.7. Minimal transformations. 6.8. Summary and suggested reading
- 7. Signal-flow graphs. 7.1. The signal-flow graph. 7.2. Topological evaluation of determinants. 7.3. Topological evaluation of cofactors. 7.4. Topological solutions of linear algebraic equations. 7.5. Equivalence and transformation. 7.6. The matrix inversion. 7.7. Signal-flow graph formulation of feedback amplifier theory. 7.8. Matrix signal-flow graph. 7.9. The multiple-loop feedback amplifier theory. 7.10. Summary and suggested reading
- 8. Other net applications. 8.1. Boolean matrices and switching nets. 8.2. Tellegen's theorem. 8.3. Generalized signal-flow graphs. 8.4. Permutations by spaghetti Amida. 8.5. The Amida graph. 8.6. Graph decomposition and hybrid analysis of electrical networks. 8.7. Summary and suggested reading.