Algebraic algorithms in combinatorial optimization.

• Other Authors: Cheung, Ho Yee.
• Format: Others
• Language: English; Chinese
• Published: 2011
• Subjects: Combinatorial optimization; Algebra; Algorithms
• Online Access: http://library.cuhk.edu.hk/record=b5894607; http://repository.lib.cuhk.edu.hk/en/item/cuhk-327410

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