Browsing Combinatorics and Optimization by Type "Doctoral Thesis"
Now showing items 1-20 of 122
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Algebraic Aspects of Multi-Particle Quantum Walks
(University of Waterloo, 2012-12-04)A continuous time quantum walk consists of a particle moving among the vertices of a graph G. Its movement is governed by the structure of the graph. More formally, the adjacency matrix A is the Hamiltonian that determines ... -
Algebraic Methods and Monotone Hurwitz Numbers
(University of Waterloo, 2012-09-21)We develop algebraic methods to solve join-cut equations, which are partial differential equations that arise in the study of permutation factorizations. Using these techniques, we give a detailed study of the recently ... -
Analyzing Quantum Cryptographic Protocols Using Optimization Techniques
(University of Waterloo, 2012-05-22)This thesis concerns the analysis of the unconditional security of quantum cryptographic protocols using convex optimization techniques. It is divided into the study of coin-flipping and oblivious transfer. We first examine ... -
Approximation Algorithms for Clustering and Facility Location Problems
(University of Waterloo, 2017-04-06)Facility location problems arise in a wide range of applications such as plant or warehouse location problems, cache placement problems, and network design problems, and have been widely studied in Computer Science and ... -
Approximation Algorithms for Distributionally Robust Stochastic Optimization
(University of Waterloo, 2019-05-15)Two-stage stochastic optimization is a widely used framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: ... -
Approximation Algorithms for Path TSP, ATSP, and TAP via Relaxations
(University of Waterloo, 2015-07-29)Linear programming (LP) relaxations provide a powerful technique to design approximation algorithms for combinatorial optimization problems. In the first part of the thesis, we study the metric s-t path Traveling Salesman ... -
Bipartite Distance-Regular Graphs of Diameter Four
(University of Waterloo, 2014-08-11)Using a method by Godsil and Roy, bipartite distance-regular graphs of diameter four can be used to construct $\{0,\alpha\}$-sets, a generalization of the widely applied equiangular sets and mutually unbiased bases. In ... -
Bipartite Quantum Walks and the Hamiltonian
(University of Waterloo, 2023-09-26)We study a discrete quantum walk model called bipartite walks via a spectral approach. A bipartite walk is determined by a unitary matrix U, i.e., the transition matrix of the walk. For every transition matrix U, there is ... -
Brick Generation and Conformal Subgraphs
(University of Waterloo, 2016-04-15)A nontrivial connected graph is matching covered if each of its edges lies in a perfect matching. Two types of decompositions of matching covered graphs, namely ear decompositions and tight cut decompositions, have played ... -
Character Polynomials and Lagrange Inversion
(University of Waterloo, 2005)In this thesis, we investigate two expressions for symmetric group characters: Kerov?s universal character polynomials and Stanley?s character polynomials. We give a new explicit form for Kerov?s polynomials, which ... -
Classical Authenticated Key Exchange and Quantum Cryptography
(University of Waterloo, 2009-03-16)Cryptography plays an integral role in secure communication and is usually the strongest link in the chain of security. Yet security problems abound in electronic communication: spyware, phishing, denial of service, and ... -
Cliques, Degrees, and Coloring: Expanding the ω, Δ, χ paradigm
(University of Waterloo, 2019-08-09)Many of the most celebrated and influential results in graph coloring, such as Brooks' Theorem and Vizing's Theorem, relate a graph's chromatic number to its clique number or maximum degree. Currently, several of the most ... -
Combinatorial Arithmetic on Elliptic Curves
(University of Waterloo, 2017-09-27)We propose a scalar multiplication technique on an elliptic curve, which operates on triples of collinear points. The computation of this operation requires a new approach to operation chains, with similarities to Montgomery ... -
Combinatorial Constructions for Transitive Factorizations in the Symmetric Group
(University of Waterloo, 2004)We consider the problem of counting <i>transitive factorizations</i> of permutations; that is, we study tuples (σ<i>r</i>,. . . ,σ1) of permutations on {1,. . . ,<i>n</i>} such that (1) the product ... -
Combinatorial Methods for Enumerating Maps in Surfaces of Arbitrary Genus
(University of Waterloo, 2016-06-10)The problem of map enumeration is one that has been studied intensely for the past half century. Early work on this subject included the works of Tutte for various types of rooted planar maps and the works of Brown for ... -
Combinatorics of Grassmannian Decompositions
(University of Waterloo, 2019-08-22)This thesis studies several combinatorially defined families of subsets of the Grassmannian. We introduce and study a family of subsets called “basis shape loci” associated to transversal matroids. Additionally, we study ... -
The combinatorics of the Jack parameter and the genus series for topological maps
(University of Waterloo, 2009-08-19)Informally, a rooted map is a topologically pointed embedding of a graph in a surface. This thesis examines two problems in the enumerative theory of rooted maps. The b-Conjecture, due to Goulden and Jackson, predicts ... -
Comparing Intersection Cut Closures using Simple Families of Lattice-Free Convex Sets
(University of Waterloo, 2022-04-26)Mixed integer programs are a powerful mathematical tool, providing a general model for expressing both theoretically difficult and practically useful problems. One important subroutine of algorithms solving mixed integer ... -
A Comprehensive Analysis of Lift-and-Project Methods for Combinatorial Optimization
(University of Waterloo, 2014-08-20)In both mathematical research and real-life, we often encounter problems that can be framed as finding the best solution among a collection of discrete choices. Many of these problems, on which an exhaustive search in the ... -
Computing the Nucleolus of Matching and b-Matching Games
(University of Waterloo, 2021-05-21)In the classical weighted matching problem the optimizer is given a graph with edge weights and their goal is to find a matching which maximizes the sum of the weights of edges in the matching. It is typically assumed in ...