Fung, Wai Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 70-76). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Overview --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.1.1 --- Network Design --- p.1 / Chapter 1.1.2 --- Degree Bounded Network Design --- p.3 / Chapter 1.1.3 --- Degree Bounded Vertex Connectivity Network Design --- p.6 / Chapter 1.2 --- Our Results --- p.7 / Chapter 1.2.1 --- Problem Definition --- p.8 / Chapter 1.2.2 --- Main Result --- p.8 / Chapter 1.2.3 --- Organization of This Thesis --- p.9 / Chapter 1.3 --- Algorithm Outline --- p.10 / Chapter 1.3.1 --- Christofides' Algorithm for TSP --- p.10 / Chapter 1.3.2 --- Extending Christofides´ة Algorithm to K > 2 --- p.12 / Chapter 1.3.3 --- Bienstock et al´ةs Splitting-Off Theorem --- p.13 / Chapter 2 --- Basics --- p.18 / Chapter 2.1 --- Notations and Terminology --- p.18 / Chapter 2.2 --- .Menger's Theorem --- p.20 / Chapter 2.3 --- Submodular Functions --- p.21 / Chapter 2.4 --- Use of Submodularity in Proofs of Splitting-Off Theorems --- p.22 / Chapter 2.5 --- Splitting-Off Concerning Edge Connectivity --- p.27 / Chapter 2.6 --- Splitting-Off Concerning Vertex Connectivity --- p.30 / Chapter 2.7 --- Vertex Connectivity Network Design --- p.32 / Chapter 2.7.1 --- Rooted Connectivity --- p.33 / Chapter 2.7.2 --- Global Connectivity --- p.35 / Chapter 2.7.3 --- Generalized Steiner Network --- p.36 / Chapter 2.8 --- Network Design with Metric Cost --- p.37 / Chapter 2.8.1 --- Minimum Cost K-Vertex-Connected Subgraph --- p.38 / Chapter 2.8.2 --- Degree Bounded Minimum Spanning Tree --- p.40 / Chapter 3 --- Minimum Degree K-Vertex-Connected Subgraph --- p.42 / Chapter 3.1 --- Preliminary --- p.44 / Chapter 3.1.1 --- Tight Sets --- p.44 / Chapter 3.1.2 --- (xxi)-Critical Sets --- p.46 / Chapter 3.2 --- Splitting-Off with Parallel Edges --- p.47 / Chapter 3.2.1 --- When Does Replacement Fail? --- p.48 / Chapter 3.2.2 --- Deriving a Special Structure --- p.50 / Chapter 3.2.3 --- Such Structure Is Impossible --- p.50 / Chapter 3.3 --- Splitting-Off with Redundant Edges --- p.50 / Chapter 3.3.1 --- Proof Outline --- p.51 / Chapter 3.3.2 --- When Does Splitting-Off Fail? --- p.54 / Chapter 3.3.3 --- Admissible Pairs Exists If Two Redundant Edges Are Present --- p.57 / Chapter 3.3.4 --- Proof of Property(T*) --- p.58 / Chapter 3.3.5 --- Existence of Jointly Admissible Pairs --- p.62 / Chapter 3.4 --- Main Algorithm --- p.66 / Chapter 4 --- Concluding Remarks --- p.69 / Bibliography --- p.70
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326735 |
| Date | January 2009 |
| Contributors | Fung, Wai Shing., Chinese University of Hong Kong Graduate School. Division of Computer Science and Engineering. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, viii, 76 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
Page generated in 0.0014 seconds