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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Learning Quantum States Without Entangled Measurements
(University of Waterloo, 2021-10-22)How many samples of a quantum state are required to learn a complete description of it? As we will see in this thesis, the fine-grained answer depends on the measurements available to the learner, but in general it is at ... -
Local Structure for Vertex-Minors
(University of Waterloo, 2021-10-12)This thesis is about a conjecture of Geelen on the structure of graphs with a forbidden vertex-minor; the conjecture is like the Graph Minors Structure Theorem of Robertson and Seymour but for vertex-minors instead of ... -
Simple Drawings of Kn from Rotation Systems
(University of Waterloo, 2021-10-06)A complete rotation system on n vertices is a collection of n cyclic permutations of the elements [n]\{i}, for i∈[n]. If D is a drawing of a labelled graph, then a rotation at vertex v is the cyclic ordering of the edges ... -
Correspondence Colouring and its Applications to List Colouring and Delay Colouring
(University of Waterloo, 2021-09-28)In this thesis, we study correspondence colouring and its applications to list colouring and delay colouring. We give a detailed exposition of the paper of Dvořák, and Postle introducing correspondence colouring. Moreover, ... -
Thomassen’s 5-Choosability Theorem Extends to Many Faces
(University of Waterloo, 2021-09-10)We prove in this thesis that planar graphs can be L-colored, where L is a list-assignment in which every vertex has a 5-list except for a collection of arbitrarily large faces which have 3-lists, as long as those faces ... -
Decomposition-based methods for Connectivity Augmentation Problems
(University of Waterloo, 2021-09-03)In this thesis, we study approximation algorithms for Connectivity Augmentation and related problems. In the Connectivity Augmentation problem, one is given a base graph G=(V,E) that is k-edge-connected, and an additional ... -
Representations of even-cycle and even-cut matroids
(University of Waterloo, 2021-08-27)In this thesis, two classes of binary matroids will be discussed: even-cycle and even-cut matroids, together with problems which are related to their graphical representations. Even-cycle and even-cut matroids can be ... -
Algorithm Substitution Attacks: Detecting ASAs Using State Reset and Making ASAs Asymmetric
(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 ... -
Convex Algebraic Geometry Approaches to Graph Coloring and Stable Set Problems
(University of Waterloo, 2021-08-23)The objective of a combinatorial optimization problem is to find an element that maximizes a given function defined over a large and possibly high-dimensional finite set. It is often the case that the set is so large that ... -
Induced Binary Submatroids
(University of Waterloo, 2021-07-21)The notion of induced subgraphs is extensively studied in graph theory. An example is the famous Gy\'{a}rf\'{a}s-Sumner conjecture, which asserts that given a tree $T$ and a clique $K$, there exists a constant $c$ such ... -
Fractional refinements of integral theorems
(University of Waterloo, 2021-07-09)The focus of this thesis is to take theorems which deal with ``integral" objects in graph theory and consider fractional refinements of them to gain additional structure. A classic theorem of Hakimi says that for an ... -
Clifford Simulation: Techniques and Applications
(University of Waterloo, 2021-05-28)Despite the widespread belief that quantum computers cannot be efficiently simulated classically, efficient simulation is known to be possible in certain restricted regimes. In particular, the Gottesman-Knill theorem states ... -
Computing the Nucleolus of Matching and b-Matching Games
(University of Waterloo, 2021-05-21)In the classical weighted matching problem the optimizer is given a graph with edge weights and their goal is to find a matching which maximizes the sum of the weights of edges in the matching. It is typically assumed in ... -
Simple Termination Criteria for Stochastic Gradient Descent Algorithm
(University of Waterloo, 2021-04-09)Stochastic gradient descent (SGD) algorithm is widely used in modern mathematical optimization. Because of its scalability and ease of implementation, SGD is usually preferred to other methods including the gradient descent ... -
Tolls For Atomic Congestion Games
(University of Waterloo, 2021-02-26)In games where selfish players compete for resources, they often arrive at equilibria that are less desirable than the social optimum. To combat this inefficiency, it is common for some central authority to place tolls on ... -
Open Shortest Path First Routing Under Random Early Detection
(Wiley, 2018-03-01)In this article, we consider a variant of Open Shortest Path First (OSPF) routing that accounts for Random Early Detection (RED), an Active Queue Management method for backbone networks. In the version of OSPF we consider ... -
Relaxations of the Maximum Flow Minimum Cut Property for Ideal Clutters
(University of Waterloo, 2021-01-29)Given a family of sets, a covering problem consists of finding a minimum cost collection of elements that hits every set. This objective can always be bound by the maximum number of disjoint sets in the family, we refer ... -
Comparing Classical Portfolio Optimization and Robust Portfolio Optimization on Black Swan Events
(University of Waterloo, 2021-01-29)Black swan events, such as natural catastrophes and manmade market crashes, historically have a drastic negative influence on investments; and there is a discrepancy on losses caused by these two types of disasters. In ... -
Craniosynostosis Surgery: A Study of Rearrangement
(University of Waterloo, 2020-12-22)Cranial vault remodeling, a form of skull surgery is currently performed according to intuition developed over years of experience. The problem of how to best perform this surgery has not yet thoroughly been studied by ... -
Quantum Compression and Quantum Learning via Information Theory
(University of Waterloo, 2020-12-21)This thesis consists of two parts: quantum compression and quantum learning theory. A common theme between these problems is that we study them through the lens of information theory. We first study the task of visible ...
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