Yung, Chun Kong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 121-129). / Abstracts in English and Chinese. / Chapter 1 --- Overview --- p.2 / Chapter 2 --- Background --- p.7 / Chapter 2.1 --- Graphs and Edge-connectivitv --- p.7 / Chapter 2.1.1 --- Subgraphs --- p.9 / Chapter 2.1.2 --- Cut and Edge-Connectivitv --- p.10 / Chapter 2.1.3 --- Menger's Theorem --- p.12 / Chapter 2.2 --- Edge Splitting-off --- p.13 / Chapter 2.2.1 --- The Basics --- p.15 / Chapter 2.2.1.1 --- Supermodular and Submodular Set Functions --- p.16 / Chapter 2.2.1.2 --- Set Functions regarding Edge-Connectivity --- p.17 / Chapter 2.2.1.3 --- Dangerous and Tight Sets --- p.18 / Chapter 2.2.2 --- Proof of Mader's Theorem --- p.20 / Chapter 2.2.3 --- Global Arc-Connectivity Setting --- p.23 / Chapter 2.2.3.1 --- Local Arc-Connectivity Setting --- p.25 / Chapter 2.2.4 --- Incorporating Additional Properties --- p.26 / Chapter 2.2.4.1 --- Non-Admissibility Graph Method --- p.27 / Chapter 2.3 --- Edge-Connectivity Problems --- p.29 / Chapter 2.3.1 --- Degree Bounded Network Design Problems --- p.30 / Chapter 2.3.1.1 --- Metric Cost Assumption --- p.31 / Chapter 2.3.2 --- Edge-Connectivitv Augmentation Problems --- p.33 / Chapter 2.3.2.1 --- Prank's Framework --- p.34 / Chapter 2.3.2.2 --- Constrained Edge-Connectivity Augmentation Problems --- p.36 / Chapter 2.3.3 --- Edge Splitting-off Problems --- p.39 / Chapter 2.4 --- Edge Splitting-off Algorithms --- p.40 / Chapter 2.4.1 --- Fastest Algorithms --- p.41 / Chapter 2.4.2 --- An Intuitive Approach --- p.42 / Chapter 2.4.3 --- Global Connectivity Settings --- p.42 / Chapter 2.4.3.1 --- Legal Ordering --- p.43 / Chapter 2.4.3.2 --- Edmonds' Arborescences --- p.44 / Chapter 2.4.4 --- Local Edge-Connectivity Setting --- p.45 / Chapter 3 --- Degree Bounded Network Design Problem with Metric Cost --- p.47 / Chapter 3.1 --- Christofides'-like Algorithm --- p.49 / Chapter 3.2 --- Simplicity-Preserving Edge Splitting-Off --- p.50 / Chapter 3.2.1 --- Proof of Theorem 3.3 --- p.51 / Chapter 3.3 --- Approximation Algorithms for Network Design Problems --- p.56 / Chapter 3.3.1 --- Removing Redundant Edges --- p.57 / Chapter 3.3.2 --- Perfect Matching --- p.58 / Chapter 3.3.3 --- Edge Splitting-Off Restoring Simplicity --- p.59 / Chapter 3.4 --- Results in Different Settings --- p.60 / Chapter 3.4.1 --- Global Edge-Connectivity --- p.61 / Chapter 3.4.2 --- Local Edge-Connectivity --- p.62 / Chapter 4 --- Constrained Edge Splitting-off --- p.64 / Chapter 4.1 --- Preliminaries --- p.66 / Chapter 4.2 --- General Constrained Edge Splitting-off Lemma --- p.68 / Chapter 4.3 --- Structural Properties of Non-Admissible Pairs --- p.69 / Chapter 4.3.1 --- Some Useful Lemmas --- p.70 / Chapter 4.3.2 --- An Upper Bound on \Dp\ --- p.71 / Chapter 4.3.3 --- An Inductive Argument --- p.73 / Chapter 4.4 --- Non-Admissibility Graph and Constraint Graph --- p.75 / Chapter 4.4.1 --- Vertex Set Partition Constraint --- p.76 / Chapter 4.4.2 --- Graph Simplicity Constraint --- p.77 / Chapter 4.4.3 --- Simultaneous Graph Constraint --- p.78 / Chapter 4.4.4 --- Tight Sufficient Conditions --- p.79 / Chapter 4.5 --- Global Arc-Connectivity Setting --- p.79 / Chapter 4.5.1 --- Proof of Lemma 4.15 --- p.81 / Chapter 5 --- Constrained Edge-Connectivity Augmentation Problem --- p.83 / Chapter 5.1 --- Preliminaries --- p.84 / Chapter 5.2 --- Additive Approximation Algorithms --- p.87 / Chapter 5.2.1 --- Edge-Connectivitv Augmentation Preserving Vertex Set Partition --- p.87 / Chapter 5.2.2 --- Edge-Connectivity Augmentation Preserving Simplicity --- p.91 / Chapter 5.2.3 --- Simultaneous-Graph Edge-Connectivity Augmentation --- p.93 / Chapter 5.3 --- Global Arc-Connectivity Setting --- p.95 / Chapter 5.3.1 --- Edge-Connectivity Augmentation Preserving Vertex Set Partition --- p.95 / Chapter 5.3.2 --- Edge-Connectivity Augmentation Preserving Simplicity --- p.97 / Chapter 5.3.3 --- Simultaneous Edge-Connectivity Augmentation --- p.98 / Chapter 6 --- Efficient Edge Splitting-off Algorithm --- p.100 / Chapter 6.l --- Preliminaries --- p.102 / Chapter 6.1.1 --- Efficient Tools for Edge-Connectivity Problems --- p.103 / Chapter 6.1.2 --- An Alternative Proof of Mader's Theorem --- p.104 / Chapter 6.2 --- Framework for Complete Edge Splitting-off --- p.105 / Chapter 6.2.1 --- Proof of Lemma 6.5 --- p.106 / Chapter 6.3 --- Efficient Splitting-off Attempt --- p.108 / Chapter 6.3.1 --- Indicator Vertex --- p.109 / Chapter 6.3.2 --- Splitting-off to Capacity --- p.112 / Chapter 6.4 --- Randomized and Parallelized Edge Splitting-off Algorithm --- p.113 / Chapter 6.5 --- Deterministic Edge Splitting-off Algorithm --- p.114 / Chapter 6.6 --- Algorithms in Other Settings --- p.115 / Chapter 6.6.1 --- Edge Splitting-off in Network Design Problems --- p.115 / Chapter 6.6.2 --- Constrained Edge Splitting-off --- p.116 / Chapter 7 --- Concluding Remarks --- p.119 / Bibliography --- p.121
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326778 |
| Date | January 2009 |
| Contributors | Yung, Chun Kong., 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, ix, 129 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/) |
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