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.
Recent deposits

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 ... 
Nearoptimal quantum strategies for nonlocal games, approximate representations, and BCS algebras
(University of Waterloo, 20230504)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 ... 
NonAdaptive Matroid Prophet Inequalities
(University of Waterloo, 20230504)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 2competitive mechanism for all the matroids. However, the ... 
Semidefinite Programming Relaxations of the Simplified Wasserstein Barycenter Problem: An ADMM Approach
(University of Waterloo, 20230504)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
(University of Waterloo, 20230501)In combinatorial markets where buyers are selfinterested, 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
(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 ... 
On coloring digraphs with forbidden induced subgraphs
(University of Waterloo, 20230425)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 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 ...