Browsing Combinatorics and Optimization by Title
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2crossing critical graphs with a V8 minor
(University of Waterloo, 20120117)The crossing number of a graph is the minimum number of pairwise crossings of edges among all planar drawings of the graph. A graph G is kcrossing critical if it has crossing number k and any proper subgraph of G has a ... 
5Choosability of Planarplustwoedge Graphs
(University of Waterloo, 20180102)We prove that graphs that can be made planar by deleting two edges are 5choosable. To arrive at this, first we prove an extension of a theorem of Thomassen. Second, we prove an extension of a theorem Postle and Thomas. ... 
Action of degenerate Bethe operators on representations of the symmetric group
(University of Waterloo, 20180524)Degenerate Bethe operators are elements defined by explicit sums in the center of the group algebra of the symmetric group. They are useful on account of their relation to the GelfandZetlin algebra and the YoungJucysMurphy ... 
Acyclic Colouring of Graphs on Surfaces
(University of Waterloo, 20180904)An acyclic kcolouring of a graph G is a proper kcolouring of G with no bichromatic cycles. In 1979, Borodin proved that planar graphs are acyclically 5colourable, an analog of the Four Colour Theorem. Kawarabayashi and ... 
ADMM for SDP Relaxation of GP
(University of Waterloo, 20160830)We consider the problem of partitioning the set of nodes of a graph G into k sets of given sizes in order to minimize the cut obtained after removing the kth set. This is a variant of the wellknown vertex separator ... 
Algebraic Analysis of VertexDistinguishing EdgeColorings
(University of Waterloo, 2006)Vertexdistinguishing edgecolorings (vdec colorings) are a restriction of proper edgecolorings. These special colorings require that the sets of edge colors incident to every vertex be distinct. This is a relatively ... 
Algebraic and combinatorial aspects of incidence groups and linear system nonlocal games arising from graphs
(University of Waterloo, 20190606)To every linear binaryconstraint system (LinBCS) nonlocal game, there is an associated algebraic object called the solution group. Cleve, Liu, and Slofstra showed that a LinBCS game has a perfect quantum strategy if and ... 
Algebraic Aspects of MultiParticle Quantum Walks
(University of Waterloo, 20121204)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, 20120921)We develop algebraic methods to solve joincut 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 ... 
Algebraic Methods for Reducibility in NowhereZero Flows
(University of Waterloo, 20070925)We study reducibility for nowherezero flows. A reducibility proof typically consists of showing that some induced subgraphs cannot appear in a minimum counterexample to some conjecture. We derive algebraic proofs of ... 
Algebraic Tori in Cryptography
(University of Waterloo, 2005)Communicating bits over a network is expensive. Therefore, cryptosystems that transmit as little data as possible are valuable. This thesis studies several cryptosystems that require significantly less bandwidth than ... 
Algorithm Design for Ordinal Settings
(University of Waterloo, 20220829)Social choice theory is concerned with aggregating the preferences of agents into a single outcome. While it is natural to assume that agents have cardinal utilities, in many contexts, we can only assume access to the ... 
An Algorithm for Stable Matching with Approximation up to the Integrality Gap
(University of Waterloo, 20200710)In the stable matching problem we are given a bipartite graph G = (A ∪ B, E) where A and B represent disjoint groups of agents, each of whom has ordinal preferences over the members of the opposite group. The goal is to ... 
Algorithm Substitution Attacks: Detecting ASAs Using State Reset and Making ASAs Asymmetric
(University of Waterloo, 20210827)The field of cryptography has made incredible progress in the last several decades. With the formalization of security goals and the methods of provable security, we have achieved many privacy and integrity guarantees in ... 
Algorithmic and Linear ProgrammingBased Techniques for the Maximum Utility Problem
(University of Waterloo, 20230525)A common topic of study in the subfield of Operations Research known as Revenue Management is finding optimal prices for a line of products given customer preferences. While there exists a large number of ways to model ... 
Algorithms for Analytic Combinatorics in Several Variables
(University of Waterloo, 20230425)Given a multivariate rational generating function we are interested in computing asymptotic formulas for the sequences encoded by the coefficients. In this thesis we apply the theory of analytic combinatorics in several ... 
Analyzing Quantum Cryptographic Protocols Using Optimization Techniques
(University of Waterloo, 20120522)This thesis concerns the analysis of the unconditional security of quantum cryptographic protocols using convex optimization techniques. It is divided into the study of coinflipping and oblivious transfer. We first examine ... 
Analyzing Tree Attachments in 2CrossingCritical Graphs with a V8 Minor
(University of Waterloo, 20230425)The crossing number of a graph is the minimum number of pairwise edge crossings in a drawing of the graph in the plane. A graph G is kcrossingcritical if its crossing number is at least k and if every proper subgraph H ... 
Applications of Bilinear Maps in Cryptography
(University of Waterloo, 2002)It was recently discovered by Joux [30] and Sakai, Ohgishi and Kasahara [47] that bilinear maps could be used to construct cryptographic schemes. Since then, bilinear maps have been used in applications as varied as ... 
Applications of Semidefinite Programming in Quantum Cryptography
(University of Waterloo, 20070518)Coinflipping is the cryptographic task of generating a random coinflip between two mistrustful parties. Kitaev discovered that the security of quantum coinflipping protocols can be analyzed using semidefinite programming. ...