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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).

### Recent deposits

• #### STPA-Sec Applied to Path Planning: Quantum-Safe Autonomous Vehicles ﻿

(University of Waterloo, 2022-05-12)
Autonomous vehicles and quantum computers are two emerging technologies that will transform our world in the not-too-distant future. This thesis examines the safety and security of autonomous vehicles in a world where ...
• #### Assessing the Trainability of the Variational Quantum State Diagonalization Algorithm at Scale ﻿

(University of Waterloo, 2022-04-28)
Quantum algorithm development is a famously difficult problem. The lack of intuition concerning the quantum realm makes constructing quantum algorithms which solve partic- ular problems of interest difficult. In addition, ...
• #### Comparing Intersection Cut Closures using Simple Families of Lattice-Free Convex Sets ﻿

(University of Waterloo, 2022-04-26)
Mixed integer programs are a powerful mathematical tool, providing a general model for expressing both theoretically difficult and practically useful problems. One important subroutine of algorithms solving mixed integer ...
• #### An Isogeny-Based Adaptor Signature Using SQISign ﻿

(University of Waterloo, 2022-04-19)
Transactions on blockchains can prove very costly, so as a solution to avoid these large costs, schemes involving payment channel networks have been developed. One approach to implementing these off-chain forms of payment ...
• #### Coloring Algorithms for Graphs and Hypergraphs with Forbidden Substructures ﻿

(University of Waterloo, 2022-04-18)
This thesis mainly focus on complexity results of the generalized version of the $r$-Coloring Problem, the $r$-Pre-Coloring Extension Problem and the List $r$-Coloring Problem restricted to hypergraphs and ordered graphs ...
• #### Vertex Stabilizers for Network Bargaining Games ﻿

(University of Waterloo, 2022-03-04)
Network bargaining games form a prominent class of examples of game theory problems defined on graphs, where vertices represent players, and edges represent their possible interactions. An instance of a \emph{network ...
• #### Minimum Number of Triangles of K5 Descendants ﻿

(University of Waterloo, 2022-01-26)
In the study of Quantum Field Theory and Feynman Periods, the operation of double triangle expansion plays an important role. This is largely due to double triangle expansions not affecting the maximum weight of the ...
• #### A Combinatorial Tale of Two Scattering Amplitudes: See Two Bijections ﻿

(University of Waterloo, 2022-01-07)
In this thesis, we take a journey through two different but not dissimilar stories with an underlying theme of combinatorics emerging from scattering amplitudes in quantum field theories. The first part tells the tale ...
• #### On Finding Large Cliques when the Chromatic Number is close to the Maximum Degree ﻿

(University of Waterloo, 2021-12-23)
We prove that every graph G with chromatic number χ(G) = ∆(G) − 1 and ∆(G) ≥ 66 contains a clique of size ∆(G) − 17. Our proof closely parallels a proof from Cranston and Rabern, who showed that graphs with χ = ∆ and ∆ ≥ ...
• #### Moments of Random Quantum Circuits and Applications in Random Circuit Sampling ﻿

(University of Waterloo, 2021-12-23)
Random quantum circuits and random circuit sampling (RCS) have recently garnered tremendous attention from all sub-fields of the quantum information community, especially after Google’s quantum supremacy announcement in ...
• #### Recovery Guarantees for Graph Clustering Problems ﻿

(University of Waterloo, 2021-12-06)
Graph clustering is widely-studied unsupervised learning problem in which the task is to group similar entities together based on observed pairwise entity interactions. This problem has applications in diverse domains such ...
• #### 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 ...

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