Now showing items 1-20 of 324

    • Thomassen’s 5-Choosability Theorem Extends to Many Faces 

      Nevin, Joshua (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 

      Neogi, Rian (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 

      Heo, Cheolwon (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 

      Hodges, Philip (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 

      Romero Barbosa, Julian Ariel (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 

      Nomoto, Kazuhiro (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 

      Moore, Benjamin (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 

      Kerzner, Alexander (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 

      Toth, William Justin (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 

      Baghal, Sina (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 

      Stoll, Alexander (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 

      Liu, Jiaxin; Dimitrov, Stanko (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 

      Ferchiou, Zouhaier (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 

      Yu, Lanlan (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 

      Drygala, Marina (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 

      Bab Hadiashar, Shima (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 ...
    • A Blueprint for Semidefinite Relaxations of Binary-Constrained Quadratic Programs Computing tight bounds on NP-hard problems using ADMM 

      Graham, Naomi (University of Waterloo, 2020-12-18)
      This thesis looks at the solution techniques of two NP-hard, large scale problems, the quadratic assignment problem, QAP, and the side chain positioning, SCP, problem. We summarize existing approaches from and look at the ...
    • The complexity of some set-partitioning formulations for the vehicle routing problem with stochastic demands 

      Gunter, Joshua (University of Waterloo, 2020-10-28)
      The capacitated vehicle routing problem with stochastic demands (CVRPSD) is a variant of the deterministic capacitated vehicle routing problem (CVRP). The CVRP consists of planning routes for vehicles with a given capacity ...
    • On Combinatorics, Integrability and Puzzles 

      Miller, Timothy (University of Waterloo, 2020-10-23)
      In the last decade, many old and new results in combinatorics have been shown using the theory of quantum integrable systems from particle physics. The key to solving such problems is the derivation of an underlying ...
    • Sum-of-norms clustering: theoretical guarantee and post-processing 

      Jiang, Tao (University of Waterloo, 2020-09-11)
      Sum-of-norms clustering is a method for assigning n points in d-dimensional real space to K clusters, using convex optimization. Recently, Panahi et al. proved that sum-of-norms clustering is guaranteed to recover a mixture ...

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