Browsing Combinatorics and Optimization by Title
Now showing items 93-112 of 436
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Contributions at the Interface Between Algebra and Graph Theory
(University of Waterloo, 2013-01-07)In this thesis, we make some contributions at the interface between algebra and graph theory. In Chapter 1, we give an overview of the topics and also the definitions and preliminaries. In Chapter 2, we estimate the ... -
Convergence Analysis of Generalized Primal-Dual Interior-Point Algorithms for Linear Optimization
(University of Waterloo, 2002)We study the zeroth-, first-, and second-order algorithms proposed by Tuncel. The zeroth-order algorithms are the generalization of the classic primal-dual affine-scaling methods, and have a strong connection with the ... -
Convex Algebraic Geometry Approaches to Graph Coloring and Stable Set Problems
(University of Waterloo, 2021-08-23)The objective of a combinatorial optimization problem is to find an element that maximizes a given function defined over a large and possibly high-dimensional finite set. It is often the case that the set is so large that ... -
Convex Optimization via Domain-Driven Barriers and Primal-Dual Interior-Point Methods
(University of Waterloo, 2017-08-24)This thesis studies the theory and implementation of infeasible-start primal-dual interior-point methods for convex optimization problems. Convex optimization has applications in many fields of engineering and science such ... -
Convex relaxation for the planted clique, biclique, and clustering problems
(University of Waterloo, 2011-08-24)A clique of a graph G is a set of pairwise adjacent nodes of G. Similarly, a biclique (U, V ) of a bipartite graph G is a pair of disjoint, independent vertex sets such that each node in U is adjacent to every node in V ... -
Cops and Robber Game with a Fast Robber
(University of Waterloo, 2011-03-24)Graph searching problems are described as games played on graphs, between a set of searchers and a fugitive. Variants of the game restrict the abilities of the searchers and the fugitive and the corresponding search number ... -
Core Structures in Random Graphs and Hypergraphs
(University of Waterloo, 2013-08-30)The k-core of a graph is its maximal subgraph with minimum degree at least k. The study of k-cores in random graphs was initiated by Bollobás in 1984 in connection to k-connected subgraphs of random graphs. Subsequently, ... -
Correspondence Colouring and its Applications to List Colouring and Delay Colouring
(University of Waterloo, 2021-09-28)In this thesis, we study correspondence colouring and its applications to list colouring and delay colouring. We give a detailed exposition of the paper of Dvořák, and Postle introducing correspondence colouring. Moreover, ... -
A Counterexample to a Conjecture About Triangle-Free Induced Subgraphs of Graphs with Large Chromatic Number
(Elsevier ScienceDirect, 2023-01)We prove that for every n, there is a graph G with χ(G) ≥ n and ω(G) ≤ 3 such that every induced subgraph H of G with ω(H) ≤ 2 satisfies χ(H) ≤ 4.This disproves a well-known conjecture. Our construction is a digraph with ... -
Counting Bases
(University of Waterloo, 2004)A theorem of Edmonds characterizes when a pair of matroids has a common basis. Enumerating the common bases of a pair of matroid is a much harder problem, and includes the #P-complete problem of counting the number of ... -
Counting Pentagons in Triangle-free Binary Matroids
(University of Waterloo, 2020-07-30)A rank-n binary matroid is a spanning subset E of F₂ⁿ\{0}, a triangle is a set of three elements from E which sum to zero, and the density of a rank-n binary matroid is |E|/2ⁿ. We begin by giving a new exposition of a ... -
Covering Graphs and Equiangular Tight Frames
(University of Waterloo, 2016-09-02)Recently, there has been huge attention paid to equiangular tight frames and their constructions, due to the fact that the relationship between these frames and quantum information theory was established. One of the problems ... -
Covering Problems via Structural Approaches
(University of Waterloo, 2011-09-30)The minimum set cover problem is, without question, among the most ubiquitous and well-studied problems in computer science. Its theoretical hardness has been fully characterized--logarithmic approximability has been ... -
Craniosynostosis Surgery: A Study of Rearrangement
(University of Waterloo, 2020-12-22)Cranial vault remodeling, a form of skull surgery is currently performed according to intuition developed over years of experience. The problem of how to best perform this surgery has not yet thoroughly been studied by ... -
Cross-monotonic Cost-Sharing Methods for Network Design Games
(University of Waterloo, 2007-09-26)In this thesis we consider some network design games that arise from common network design problems. A network design game involves multiple players who control nodes in a network, each of which has a personal interest ... -
Cryptography and Privacy in Vehicular Communication Networks
(University of Waterloo, 2023-08-28)Wireless communication technologies can support dynamic networks between vehicles, pedestrians and roadside infrastructure called Vehicular Ad hoc Networks (VANETs). Wireless communication over VANETs allows for several ... -
The Cycle Spaces of an Infinite Graph
(University of Waterloo, 2006)The edge space of a finite graph <em>G</em> = (<em>V</em>, <em>E</em>) over a field F is simply an assignment of field elements to the edges of the graph. The edge space can equally be thought of us an |<em>E</em>|-dimensional ... -
Cycles and coloring in graphs and digraphs
(University of Waterloo, 2022-08-22)We show results in areas related to extremal problems in directed graphs. The first concerns a rainbow generalization of the Caccetta-H\"{a}ggkvist conjecture, made by Aharoni. The Caccetta-H\"{a}ggkvist conjecture states ... -
Cyclic Sieving Phenomenon of Promotion on Rectangular Tableaux
(University of Waterloo, 2012-09-28)Cyclic sieving phenomenon (CSP) is a generalization by Reiner, Stanton, White of Stembridge's q=-1 phenomenon. When CSP is exhibited, orbits of a cyclic action on combinatorial objects show a nice structure and their sizes ... -
Cyclically 5-Connected Graphs
(University of Waterloo, 2016-08-29)Tutte's Four-Flow Conjecture states that every bridgeless, Petersen-free graph admits a nowhere-zero 4-flow. This hard conjecture has been open for over half a century with no significant progress in the first forty years. ...