Browsing Combinatorics and Optimization by Issue Date
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Differential Equations and Depth First Search for Enumeration of Maps in Surfaces
(University of Waterloo, 1999)A map is an embedding of the vertices and edges of a graph into a compact 2manifold such that the remainder of the surface has components homeomorphic to open disks. With the goal of proving the Four Colour Theorem, ... 
Variational Spectral Analysis
(University of Waterloo, 2000)We present results on smooth and nonsmooth variational properties of {it symmetric} functions of the eigenvalues of a real symmetric matrix argument, as well as {it absolutely symmetric} functions of the singular values ... 
A survey on Traitor Tracing Schemes
(University of Waterloo, 2000)When intellectual properties are distributed over a broadcast network, the content is usually encrypted in a way such that only authorized users who have a certain set of keys, can decrypt the content. Some authorized ... 
A survey of the trust region subproblem within a semidefinite framework
(University of Waterloo, 2000)Trust region subproblems arise within a class of unconstrained methods called trust region methods. The subproblems consist of minimizing a quadratic function subject to a norm constraint. This thesis is a survey of ... 
Matrix Formulations of Matching Problems
(University of Waterloo, 2000)Finding the maximum size of a matching in an undirected graph and finding the maximum size of branching in a directed graph can be formulated as matrix rank problems. The Tutte matrix, introduced by Tutte as a representation ... 
Techniques of Side Channel Cryptanalysis
(University of Waterloo, 2001)The traditional model of cryptography examines the security of cryptographic primitives as mathematical functions. This approach does not account for the physical side effects of using these primitives in the real world. ... 
New Convex Relaxations for the Maximum Cut and VLSI Layout Problems
(University of Waterloo, 2001)It is well known that many of the optimization problems which arise in applications are <I>hard</I>, which usually means that they are NPhard. Hence much research has been devoted to finding <I>good</I> relaxations for ... 
Parking Functions and Related Combinatorial Structures.
(University of Waterloo, 2001)The central topic of this thesis is parking functions. We give a survey of some of the current literature concerning parking functions and focus on their interaction with other combinatorial objects; namely noncrossing ... 
The Existence of Balanced Tournament Designs and Partitioned Balanced Tournament Designs
(University of Waterloo, 2001)A balanced tournament design of order <I>n</I>, BTD(<I>n</I>), defined on a 2<I>n</I>set<I> V</i>, is an arrangement of the all of the (2<I>n</i>2) distinct unordered pairs of elements of <I>V</I> into an <I>n</I> X ... 
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 ... 
Convergence Analysis of Generalized PrimalDual InteriorPoint Algorithms for Linear Optimization
(University of Waterloo, 2002)We study the zeroth, first, and secondorder algorithms proposed by Tuncel. The zerothorder algorithms are the generalization of the classic primaldual affinescaling methods, and have a strong connection with the ... 
Hamilton Paths in Generalized Petersen Graphs
(University of Waterloo, 2002)This thesis puts forward the conjecture that for <i>n</i> > 3<i>k</i> with <i>k</i> > 2, the generalized Petersen graph, <i>GP</i>(<i>n,k</i>) is Hamiltonlaceable if <i>n</i> is even and <i>k</i> is odd, and it is ... 
Digital Signature Scheme Variations
(University of Waterloo, 2002)A digital signature scheme is the process of signing an electronic message that can be transmitted over a computer network. Digital signatures provide message authentication that can be proved to a third party. With ... 
Continuoustime 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 NPcomplete problems e. g. 3SAT. Even so, the best known quantum ... 
SelfDual Graphs
(University of Waterloo, 2002)The study of selfduality has attracted some attention over the past decade. A good deal of research in that time has been done on constructing and classifying all selfdual graphs and in particular polyhedra. We ... 
Postman Problems on Mixed Graphs
(University of Waterloo, 2003)The <i>mixed postman problem</i> consists of finding a minimum cost tour of a mixed graph <i>M</i> = (<i>V</i>,<i>E</i>,<i>A</i>) traversing all its edges and arcs at least once. We prove that two wellknown linear ... 
Uniqueness and Complexity in Generalised Colouring
(University of Waterloo, 2003)The study and recognition of graph families (or graph properties) is an essential part of combinatorics. Graph colouring is another fundamental concept of graph theory that can be looked at, in large part, as the recognition ... 
Perfect Hash Families: Constructions and Applications
(University of Waterloo, 2003)Let <b>A</b> and <b>B</b> be finite sets with <b>A</b>=<i>n</i> and <b>B</b>=<i>m</i>. An (<i>n</i>,<i>m</i>,<i>w</i>)<i>perfect hash</i> family</i> is a collection <i>F</i> of functions from <b>A</b> to <b>B</b> ... 
An Optimizing Pulse Sequence Compiler for NMR QIP
(University of Waterloo, 2003)Quantum information processing is a multidisciplinary science involving physics, mathematics, computer science, and even quantum chemistry. It is centred around the idea of manipulating physical systems at the quantum ... 
Independent Sets and Eigenspaces
(University of Waterloo, 2004)The problems we study in this thesis arise in computer science, extremal set theory and quantum computing. The first common feature of these problems is that each can be reduced to characterizing the independent sets ...