Now showing items 1-20 of 252

    • 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 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 ...
    • Analyzing Quantum Cryptographic Protocols Using Optimization Techniques 

      Sikora, Jamie (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 ...
    • 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 ...
    • Applications of Semidefinite Programming in Quantum Cryptography 

      Sikora, Jamie William Jonathon (University of Waterloo, 2007-05-18)
      Coin-flipping is the cryptographic task of generating a random coin-flip between two mistrustful parties. Kitaev discovered that the security of quantum coin-flipping protocols can be analyzed using semidefinite programming. ...
    • Applied Hilbert's Nullstellensatz for Combinatorial Problems 

      Romero Barbosa, Julian (University of Waterloo, 2016-09-23)
      Various feasibility problems in Combinatorial Optimization can be stated using systems of polynomial equations. Determining the existence of a \textit{stable set} of a given size, finding the \textit{chromatic number} of ...
    • Approximate Private Quantum Channels 

      Dickinson, Paul (University of Waterloo, 2006)
      This thesis includes a survey of the results known for private and approximate private quantum channels. We develop the best known upper bound for &epsilon;-randomizing maps, <em>n</em> + 2log(1/&epsilon;) + <em>c</em> ...
    • Approximating Minimum-Size 2-Edge-Connected and 2-Vertex-Connected Spanning Subgraphs 

      Narayan, Vishnu Verambudi (University of Waterloo, 2017-04-27)
      We study the unweighted 2-edge-connected and 2-vertex-connected spanning subgraph problems. A graph is 2-edge-connected if it is connected on removal of an edge, and it is 2-vertex-connected if it is connected on removal ...
    • Approximation Algorithms for (S,T)-Connectivity Problems 

      Laekhanukit, Bundit (University of Waterloo, 2010-08-03)
      We study a directed network design problem called the $k$-$(S,T)$-connectivity problem; we design and analyze approximation algorithms and give hardness results. For each positive integer $k$, the minimum cost $k$-vertex ...
    • Approximation Algorithms for Clustering and Facility Location Problems 

      Ahmadian, Sara (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 Graph Protection Problems 

      Lange, Alexander (University of Waterloo, 2015-05-22)
      We study a budgeted cut problem known as Graph Protection, where the goal is to remove edges of a given graph in order to protect valuable nodes from stochastic, infectious threats. This problem was recently proposed ...
    • Approximation Algorithms for Path TSP, ATSP, and TAP via Relaxations 

      Gao, Zhihan (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 ...

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