Cheung, Ho Yee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 91-96). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background --- p.5 / Chapter 2.1 --- Matroids and Matrices --- p.5 / Chapter 2.1.1 --- Examples --- p.6 / Chapter 2.1.2 --- Constructions --- p.7 / Chapter 2.1.3 --- Matroid Intersection --- p.8 / Chapter 2.1.4 --- Matroid Parity --- p.9 / Chapter 2.2 --- Matrix Formulations --- p.14 / Chapter 2.2.1 --- Graph Matching --- p.15 / Chapter 2.2.2 --- Skew-Symmetric Matrix --- p.16 / Chapter 2.2.3 --- Linear Matroid Parity --- p.21 / Chapter 2.2.4 --- Weighted Problems --- p.25 / Chapter 2.3 --- Algebraic Tools --- p.26 / Chapter 2.3.1 --- Matrix Algorithms --- p.26 / Chapter 2.3.2 --- Computing Matrix Inverse --- p.28 / Chapter 2.3.3 --- Matrix of Indeterminates --- p.32 / Chapter 2.3.4 --- Mixed Skew-symmetric Matrix --- p.34 / Chapter 2.4 --- Algebraic Algorithms for Graph Matching --- p.35 / Chapter 2.4.1 --- Matching in O{nw+1) time --- p.36 / Chapter 2.4.2 --- Matching in O(n3) time --- p.37 / Chapter 2.4.3 --- Matching in O(nw) time --- p.38 / Chapter 2.4.4 --- Weighted Algorithms --- p.39 / Chapter 2.4.5 --- Parallel Algorithms --- p.40 / Chapter 2.5 --- Algebraic Algorithms for Graph Connectivity --- p.41 / Chapter 2.5.1 --- Previous Approach --- p.41 / Chapter 2.5.2 --- Matrix Formulation Using Network Coding --- p.42 / Chapter 3 --- Linear Matroid Parity --- p.49 / Chapter 3.1 --- Introduction --- p.49 / Chapter 3.1.1 --- Problem Formulation and Previous Work --- p.50 / Chapter 3.1.2 --- Our Results --- p.52 / Chapter 3.1.3 --- Techniques --- p.55 / Chapter 3.2 --- Preliminaries --- p.56 / Chapter 3.3 --- A Simple Algebraic Algorithm for Linear Matroid Parity --- p.56 / Chapter 3.3.1 --- An 0(mr2) Algorithm --- p.56 / Chapter 3.4 --- Graph Algorithms --- p.59 / Chapter 3.4.1 --- Mader's S-Path --- p.59 / Chapter 3.4.2 --- Graphic Matroid Parity --- p.64 / Chapter 3.4.3 --- Colorful Spanning Tree --- p.66 / Chapter 3.5 --- Weighted Linear Matroid Parity --- p.69 / Chapter 3.6 --- A Faster Linear Matroid Parity Algorithm --- p.71 / Chapter 3.6.1 --- Matrix Formulation --- p.71 / Chapter 3.6.2 --- An O(mw) Algorithm --- p.74 / Chapter 3.6.3 --- An O(mrw - 1 ) Algorithm --- p.76 / Chapter 3.7 --- Maximum Cardinality Matroid Parity --- p.79 / Chapter 3.8 --- Open Problems --- p.80 / Chapter 4 --- Graph Connectivities --- p.81 / Chapter 4.1 --- Introduction --- p.81 / Chapter 4.2 --- Inverse of Well-Separable Matrix --- p.83 / Chapter 4.3 --- Directed Graphs with Good Separators --- p.86 / Chapter 4.4 --- Open Problems --- p.89
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_327410 |
| Date | January 2011 |
| Contributors | Cheung, Ho Yee., 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, [4], iv, 96 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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