Browsing Combinatorics and Optimization by Type "Master Thesis"
Now showing items 41-60 of 258
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Clique minors in dense matroids
(University of Waterloo, 2022-09-23)The objective of this thesis is to bound the number of points a $U_{2,\ell+2}$- and $M(K_{k+1})$-minor-free matroid has. We first prove that a sufficiently large matroid will contain a structure called a tower. We then use ... -
Collision Finding with Many Classical or Quantum Processors
(University of Waterloo, 2011-08-31)In this thesis, we investigate the cost of finding collisions in a black-box function, a problem that is of fundamental importance in cryptanalysis. Inspired by the excellent performance of the heuristic rho method of ... -
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 ... -
Colouring Cayley Graphs
(University of Waterloo, 2005)We will discuss three ways to bound the chromatic number on a Cayley graph. 1. If the connection set contains information about a smaller graph, then these two graphs are related. Using this information, we will ... -
Colouring Subspaces
(University of Waterloo, 2005)This thesis was originally motivated by considering vector space analogues of problems in extremal set theory, but our main results concern colouring a graph that is intimately related to these vector space analogues. ... -
Combinatorial Algorithms for Submodular Function Minimization and Related Problems
(University of Waterloo, 2015-05-19)Submodular functions are common in combinatorics; examples include the cut capacity function of a graph and the rank function of a matroid. The submodular function minimization problem generalizes the classical minimum cut ... -
Combinatorial Approaches To The Jacobian Conjecture
(University of Waterloo, 2007-08-24)The Jacobian Conjecture is a long-standing open problem in algebraic geometry. Though the problem is inherently algebraic, it crops up in fields throughout mathematics including perturbation theory, quantum field theory ... -
Combinatorial aspects of braids with applications to cryptography
(University of Waterloo, 2015-08-25)This thesis is a collection of different results on braids, and draws connections between them. We first introduce braids by showcasing a number of equivalent ways of describing what a braid is, and how those representations ... -
Combinatorial Generalizations of Sieve Methods and Characterizing Hamiltonicity via Induced Subgraphs
(University of Waterloo, 2022-08-17)A sieve method is in effect an application of the inclusion-exclusion counting principle, and the estimation methods to avoid computing the explicit formula. Sieve methods have been used in number theory for over a hundred ... -
A Combinatorial Interpretation of Minimal Transitive Factorizations into Transpositions for Permutations with two Disjoint Cycles
(University of Waterloo, 2008-01-24)This thesis is about minimal transitive factorizations of permutations into transpositions. We focus on finding direct combinatorial proofs for the cases where no such direct combinatorial proofs were known. We give a ... -
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 ... -
Combinatorially Thin Trees and Spectrally Thin Trees in Structured Graphs
(University of Waterloo, 2023-12-19)Given a graph $G=(V,E)$, finding simpler estimates of $G$ with possibly fewer edges or vertices while capturing some of its specific properties has been used in order to design efficient algorithms. The concept of estimating ... -
Combinatorics and the KP Hierarchy
(University of Waterloo, 2009-10-01)The study of the infinite (countable) family of partial differential equations known as the Kadomtzev - Petviashvili (KP) hierarchy has received much interest in the mathematical and theoretical physics community for ... -
Communication Complexity of Remote State Preparation
(University of Waterloo, 2014-05-27)Superdense coding and quantum teleportation are two phenomena which were not possible without prior entanglement. In superdense coding, one sends n bits of information using n/2 qubits in the presence of shared entanglement. ... -
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 ... -
The complexity of some set-partitioning formulations for the vehicle routing problem with stochastic demands
(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 ... -
A computational study of practical issues arising in short-term scheduling of a multipurpose facility
(University of Waterloo, 2019-01-23)This thesis focuses on two important considerations when solving short term scheduling problems for multipurpose facilities: deciding when rescheduling should be performed and choosing efficient time representations for ... -
Computing the Residue Class of Partition Numbers
(University of Waterloo, 2016-09-14)In 1919, Ramanujan initiated the study of congruence properties of the integer partition function $p(n)$ by showing that $$p(5n+4) \equiv 0 \mod{5}$$ and $$p(7n+5) \equiv 0 \mod{7}$$ hold for all integers $n$. These results ... -
Continuous-time Quantum Algorithms: Searching and Adiabatic Computation
(University of Waterloo, 2002)One of the most important quantum algorithms is Grover's search algorithm [G96]. Quantum searching can be used to speed up the search for solutions to NP-complete problems e. g. 3SAT. Even so, the best known quantum ... -
Contributions at the Interface Between Algebra and Graph Theory
(University of Waterloo, 2013-01-07)In this thesis, we make some contributions at the interface between algebra and graph theory. In Chapter 1, we give an overview of the topics and also the definitions and preliminaries. In Chapter 2, we estimate the ...