Combinatorics and Optimization
This is the collection for the University of Waterloo's Department of Combinatorics and Optimization .
Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).
Waterloo faculty, students, and staff can contact us or visit the UWSpace guide to learn more about depositing their research.
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Analytic Methods and Combinatorial Plants
(University of Waterloo, 20240408)Combinatorial structures have broad applications in computer science, from errorcorrecting codes to matrix multiplication. Many analytic tools have been developed for studying these structures. In this thesis, we examine ... 
GraphTheoretic Techniques for Optimizing NISQ Algorithms
(University of Waterloo, 20240215)Entering the NISQ era, the search for useful yet simple quantum algorithms is perhaps of more importance now than it may ever be in the future. In place of quantum walks, the quantum Fourier transform, and asymptotic results ... 
Formalizing the Excluded Minor Characterization of Binary Matroids in the Lean Theorem Prover
(University of Waterloo, 20240123)A matroid is a mathematical object that generalizes the notion of linear independence of a set of vectors to an abstract independence of sets, with applications to optimization, linear algebra, graph theory, and algebraic ... 
Implementing the CastryckDecru attack on SIDH with general primes
(University of Waterloo, 20240109)With the rapid progress of quantum computers in recent years, efforts have been made to standardize new publickey cryptographic protocols which would be secure against them. One of the schemes in contention was Supersingular ... 
Graphical CSS Code Transformation Using ZX Calculus
(University of Waterloo, 20231221)In this work, we present a generic approach to transform CSS codes by building upon their equivalence to phasefree ZX diagrams. Using the ZX calculus, we demonstrate diagrammatic transformations between encoding maps ... 
Combinatorially Thin Trees and Spectrally Thin Trees in Structured Graphs
(University of Waterloo, 20231219)Given a graph $G=(V,E)$, finding simpler estimates of $G$ with possibly fewer edges or vertices while capturing some of its specific properties has been used in order to design efficient algorithms. The concept of estimating ... 
Nonsmooth Newton Methods for Solving the Best Approximation Problem; with Applications to Linear Programming
(University of Waterloo, 20231219)In this thesis, we study the effects of applying a modified LevenbergMarquardt regularization to a nonsmooth Newton method. We expand this application to exact and inexact nonsmooth Newton methods and apply it to the ... 
Bipartite Quantum Walks and the Hamiltonian
(University of Waterloo, 20230926)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
(University of Waterloo, 20230921)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 MCMCbased method to address this ... 
Rigidity of nearoptimal superdense coding protocols
(University of Waterloo, 20230919)Rigidity in quantum information theory refers to the stringent constraints underlying optimal or nearoptimal performance in certain quantum tasks. This property plays a crucial role in verifying untrusted quantum devices ... 
DistanceBiregular Graphs and Orthogonal Polynomials
(University of Waterloo, 20230915)This thesis is about distancebiregular 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 distancebiregular ... 
Towards Private Biometric Authentication and Identification
(University of Waterloo, 20230905)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
(University of Waterloo, 20230901)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
(University of Waterloo, 20230828)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
(University of Waterloo, 20230828)The StanleyStembridge conjecture is a longstanding conjecture that has evaded proof for nearly 30 years. Concerned with the ebasis expansions of the chromatic symmetric functions of unitinterval graphs, this conjecture ... 
Chosen Ciphertext Security from Zero Knowledge Proofs
(University of Waterloo, 20230824)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 FrankWolfe
(University of Waterloo, 20230824)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. Stateoftheart LP solvers make use of the Simplex ... 
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 ... 
LowRank Plus Sparse Decompositions of LargeScale Matrices via Semidefinite Optimization
(University of Waterloo, 20230519)We study the problem of decomposing a symmetric matrix into the sum of a lowrank 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
(University of Waterloo, 20230518)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 ...