Now showing items 1-20 of 436

    • 2-crossing critical graphs with a V8 minor 

      Austin, Beth Ann (University of Waterloo, 2012-01-17)
      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 k-crossing critical if it has crossing number k and any proper subgraph of G has a ...
    • 5-Choosability of Planar-plus-two-edge Graphs 

      Mahmoud, Amena (University of Waterloo, 2018-01-02)
      We prove that graphs that can be made planar by deleting two edges are 5-choosable. 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 

      Rahman, Sifat (University of Waterloo, 2018-05-24)
      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 Gelfand-Zetlin algebra and the Young-Jucys-Murphy ...
    • Acyclic Colouring of Graphs on Surfaces 

      Redlin, Shayla (University of Waterloo, 2018-09-04)
      An acyclic k-colouring of a graph G is a proper k-colouring of G with no bichromatic cycles. In 1979, Borodin proved that planar graphs are acyclically 5-colourable, an analog of the Four Colour Theorem. Kawarabayashi and ...
    • ADMM for SDP Relaxation of GP 

      Sun, Hao (University of Waterloo, 2016-08-30)
      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 k-th set. This is a variant of the well-known vertex separator ...
    • Algebraic Analysis of Vertex-Distinguishing Edge-Colorings 

      Clark, David (University of Waterloo, 2006)
      Vertex-distinguishing edge-colorings (vdec colorings) are a restriction of proper edge-colorings. 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 non-local games arising from graphs 

      Paddock, Connor (University of Waterloo, 2019-06-06)
      To every linear binary-constraint system (LinBCS) non-local 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 Multi-Particle Quantum Walks 

      Smith, Jamie (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 

      Guay-Paquet, Mathieu (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 ...
    • Algebraic Methods for Reducibility in Nowhere-Zero Flows 

      Li, Zhentao (University of Waterloo, 2007-09-25)
      We study reducibility for nowhere-zero flows. A reducibility proof typically consists of showing that some induced subgraphs cannot appear in a minimum counter-example to some conjecture. We derive algebraic proofs of ...
    • Algebraic Tori in Cryptography 

      Alexander, Nicholas Charles (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 

      Pulyassary, Haripriya (University of Waterloo, 2022-08-29)
      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 

      Tofigzade, Natig (University of Waterloo, 2020-07-10)
      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 

      Hodges, Philip (University of Waterloo, 2021-08-27)
      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 Programming-Based Techniques for the Maximum Utility Problem 

      Lawrence, Paul (University of Waterloo, 2023-05-25)
      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 

      Smolcic, Josip (University of Waterloo, 2023-04-25)
      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 ...
    • Analytic Methods and Combinatorial Plants 

      Chizewer, Jeremy (University of Waterloo, 2024-04-08)
      Combinatorial structures have broad applications in computer science, from error-correcting codes to matrix multiplication. Many analytic tools have been developed for studying these structures. In this thesis, we examine ...
    • Analyzing Quantum Cryptographic Protocols Using Optimization Techniques 

      Sikora, Jamie William Jonathon (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 ...
    • Analyzing Tree Attachments in 2-Crossing-Critical Graphs with a V8 Minor 

      Bedsole, Carter (University of Waterloo, 2023-04-25)
      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 k-crossing-critical if its crossing number is at least k and if every proper subgraph H ...
    • Applications of Bilinear Maps in Cryptography 

      Gagne, Martin (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 ...


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