Browsing Combinatorics and Optimization by Title
Now showing items 16-35 of 435
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Algorithms for Analytic Combinatorics in Several Variables
(University of Waterloo, 2023-04-25)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 ... -
Analytic Methods and Combinatorial Plants
(University of Waterloo, 2024-04-08)Combinatorial structures have broad applications in computer science, from error-correcting codes to matrix multiplication. Many analytic tools have been developed for studying these structures. In this thesis, we examine ... -
Analyzing Quantum Cryptographic Protocols Using Optimization Techniques
(University of Waterloo, 2012-05-22)This thesis concerns the analysis of the unconditional security of quantum cryptographic protocols using convex optimization techniques. It is divided into the study of coin-flipping and oblivious transfer. We first examine ... -
Analyzing Tree Attachments in 2-Crossing-Critical Graphs with a V8 Minor
(University of Waterloo, 2023-04-25)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 k-crossing-critical if its crossing number is at least k and if every proper subgraph H ... -
Applications of Bilinear Maps in Cryptography
(University of Waterloo, 2002)It was recently discovered by Joux [30] and Sakai, Ohgishi and Kasahara [47] that bilinear maps could be used to construct cryptographic schemes. Since then, bilinear maps have been used in applications as varied as ... -
Applications of Semidefinite Programming in Quantum Cryptography
(University of Waterloo, 2007-05-18)Coin-flipping is the cryptographic task of generating a random coin-flip between two mistrustful parties. Kitaev discovered that the security of quantum coin-flipping protocols can be analyzed using semidefinite programming. ... -
Applications of Stochastic Gradient Descent to Nonnegative Matrix Factorization
(University of Waterloo, 2019-07-15)We consider the application of stochastic gradient descent (SGD) to the nonnegative matrix factorization (NMF) problem and the unconstrained low-rank matrix factorization problem. While the literature on the SGD algorithm ... -
Applied Hilbert's Nullstellensatz for Combinatorial Problems
(University of Waterloo, 2016-09-23)Various feasibility problems in Combinatorial Optimization can be stated using systems of polynomial equations. Determining the existence of a \textit{stable set} of a given size, finding the \textit{chromatic number} of ... -
Approximate Private Quantum Channels
(University of Waterloo, 2006)This thesis includes a survey of the results known for private and approximate private quantum channels. We develop the best known upper bound for ε-randomizing maps, <em>n</em> + 2log(1/ε) + <em>c</em> ... -
Approximately Coloring Graphs Without Long Induced Paths
(Springer Nature, 2019)It is an open problem whether the 3-coloring problem can be solved in polynomial time in the class of graphs that do not contain an induced path on t vertices, for fixed t. We propose an algorithm that, given a 3-colorable ... -
Approximately Coloring Graphs Without Long Induced Paths
(Springer Nature, 2017)It is an open problem whether the 3-coloring problem can be solved in polynomial time in the class of graphs that do not contain an induced path on t vertices, for fixed t. We propose an algorithm that, given a 3-colorable ... -
Approximating Minimum-Size 2-Edge-Connected and 2-Vertex-Connected Spanning Subgraphs
(University of Waterloo, 2017-04-27)We study the unweighted 2-edge-connected and 2-vertex-connected spanning subgraph problems. A graph is 2-edge-connected if it is connected on removal of an edge, and it is 2-vertex-connected if it is connected on removal ... -
Approximation Algorithms for (S,T)-Connectivity Problems
(University of Waterloo, 2010-08-03)We study a directed network design problem called the $k$-$(S,T)$-connectivity problem; we design and analyze approximation algorithms and give hardness results. For each positive integer $k$, the minimum cost $k$-vertex ... -
Approximation Algorithms for Clustering and Facility Location Problems
(University of Waterloo, 2017-04-06)Facility location problems arise in a wide range of applications such as plant or warehouse location problems, cache placement problems, and network design problems, and have been widely studied in Computer Science and ... -
Approximation Algorithms for Distributionally Robust Stochastic Optimization
(University of Waterloo, 2019-05-15)Two-stage stochastic optimization is a widely used framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: ... -
Approximation Algorithms for Graph Protection Problems
(University of Waterloo, 2015-05-22)We study a budgeted cut problem known as Graph Protection, where the goal is to remove edges of a given graph in order to protect valuable nodes from stochastic, infectious threats. This problem was recently proposed ... -
Approximation Algorithms for Path TSP, ATSP, and TAP via Relaxations
(University of Waterloo, 2015-07-29)Linear programming (LP) relaxations provide a powerful technique to design approximation algorithms for combinatorial optimization problems. In the first part of the thesis, we study the metric s-t path Traveling Salesman ... -
Aspects of Quantum Field Theory in Enumerative Graph Theory
(University of Waterloo, 2022-10-24)While a quantum field theorist has many uses for mathematics of all kinds, the relationship between quantum field theory and mathematics is far too fluid in the world of modern research to be described as the simple provision ... -
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, ... -
Augmenting Trees to Achieve 2-Node-Connectivity
(University of Waterloo, 2020-09-02)This thesis focuses on the Node-Connectivity Tree Augmentation Problem (NC-TAP), formally defined as follows. The first input of the problem is a graph G which has vertex set V and edge set E. We require |V| >= 3 to avoid ...