• Bipartite Quantum Walks and the Hamiltonian 

  Chen, Qiuting (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 ...

• Uniform Generation of Graphical Realizations of Joint Degree Matrices 

  Zhou, Qianye (University of Waterloo, 2023-09-21)

  In this thesis, we introduce JDM_GEN, an algorithm designed to uniformly generate graphical realizations of a given joint degree matrix. Amanatidis and Kleer previously employed an MCMC-based method to address this ...

• Rigidity of near-optimal superdense coding protocols 

  Zhou, Xingyu (University of Waterloo, 2023-09-19)

  Rigidity in quantum information theory refers to the stringent constraints underlying optimal or near-optimal performance in certain quantum tasks. This property plays a crucial role in verifying untrusted quantum devices ...

• Distance-Biregular Graphs and Orthogonal Polynomials 

  Lato, Sabrina (University of Waterloo, 2023-09-15)

  This thesis is about distance-biregular graphs– when they exist, what algebraic and structural properties they have, and how they arise in extremal problems. We develop a set of necessary conditions for a distance-biregular ...

• Towards Private Biometric Authentication and Identification 

  Gold, Jonathan (University of Waterloo, 2023-09-05)

  Handwriting and speech are important parts of our everyday lives. Handwriting recognition is the task that allows the recognizing of written text, whether it be letters, words or equations, from given data. When analyzing ...

• Enumerating matroid extensions 

  Redlin Hume, Shayla (University of Waterloo, 2023-09-01)

  This thesis investigates the problem of enumerating the extensions of certain matroids. A matroid M is an extension of a matroid N if M delete e is equal to N for some element e of M. Similarly, a matroid M is a coextension ...

• Cryptography and Privacy in Vehicular Communication Networks 

  Sharma, Pravek (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 ...

• A Linear Algebraic Method on the Chromatic Symmetric Function 

  Haithcock, Evan (University of Waterloo, 2023-08-28)

  The Stanley-Stembridge conjecture is a longstanding conjecture that has evaded proof for nearly 30 years. Concerned with the e-basis expansions of the chromatic symmetric functions of unit-interval graphs, this conjecture ...

• Chosen Ciphertext Security from Zero Knowledge Proofs 

  Steckel, Camryn (University of Waterloo, 2023-08-24)

  When designing encryption schemes, there are different levels of security that one can achieve. Of the two main security levels, cryptographers generally strive for the stronger notion of chosen ciphertext attack (CCA) ...

• Solving Saddle Point Formulations of Linear Programs with Frank-Wolfe 

  Hough, Matthew (University of Waterloo, 2023-08-24)

  The problem of solving a linear program (LP) is ubiquitous in industry, yet in recent years the size of linear programming problems has grown and continues to do so. State-of-the-art LP solvers make use of the Simplex ...

• 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 ...

• Low-Rank Plus Sparse Decompositions of Large-Scale Matrices via Semidefinite Optimization 

  Gong, Rui (University of Waterloo, 2023-05-19)

  We study the problem of decomposing a symmetric matrix into the sum of a low-rank symmetric positive semidefinite matrix and a tridiagonal matrix, and a relaxation which looks for symmetric positive semidefinite matrices ...

• Graph Coverings with Few Eigenvalues or No Short Cycles 

  Levit, Maxwell (University of Waterloo, 2023-05-18)

  This thesis addresses the extent of the covering graph construction. How much must a cover X resemble the graph Y that it covers? How much can X deviate from Y? The main statistics of X and Y which we will measure are their ...

• Near-optimal quantum strategies for nonlocal games, approximate representations, and BCS algebras 

  Paul-Paddock, Connor (University of Waterloo, 2023-05-04)

  Quantum correlations can be viewed as particular abstract states on the tensor product of operator systems which model quantum measurement scenarios. In the paradigm of nonlocal games, this perspective illustrates a ...

• Non-Adaptive Matroid Prophet Inequalities 

  Sayutina, Alice (University of Waterloo, 2023-05-04)

  We consider the problem of matroid prophet inequalities. This problem has been ex- tensively studied in case of adaptive prices, with [KW12] obtaining a tight 2-competitive mechanism for all the matroids. However, the ...

• Semidefinite Programming Relaxations of the Simplified Wasserstein Barycenter Problem: An ADMM Approach 

  Cheng, Jiahui (University of Waterloo, 2023-05-04)

  The Simplified Wasserstein Barycenter problem, the problem of picking k points each chosen from a distinct set of n points as to minimize the sum of distances to their barycenter, finds applications in various areas of ...

• Dynamic Pricing Schemes in Combinatorial Markets 

  Kalichman, David (University of Waterloo, 2023-05-01)

  In combinatorial markets where buyers are self-interested, the buyers may make purchases that lead to suboptimal item allocations. As a central coordinator, our goal is to impose prices on the items of the market so that ...

• 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 ...

• On coloring digraphs with forbidden induced subgraphs 

  Carbonero, Alvaro (University of Waterloo, 2023-04-25)

  This thesis mainly focuses on the structural properties of digraphs with high dichromatic number. The dichromatic number of a digraph $D$, denoted by $\dichi(D)$, is designed to be the directed analog of the chromatic ...

• 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 ...

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