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Now showing items 1-10 of 176

#### Quantum Speed-ups for Boolean Satisfiability and Derivative-Free Optimization

(University of Waterloo, 2014-04-21)

In this thesis, we have considered two important problems, Boolean satisfiability (SAT) and derivative free optimization in the context of large scale quantum computers. In the first part, we survey well known classical ...

#### Mathematical Programming Formulations of the Planar Facility Location Problem

(University of Waterloo, 2007-09-24)

The facility location problem is the task of optimally placing a
given number of facilities in a certain subset of the plane. In
this thesis, we present various mathematical programming
formulations of the planar ...

#### Machine-Level Software Optimization of Cryptographic Protocols

(University of Waterloo, 2014-04-30)

This work explores two methods for practical cryptography on mobile devices. The first method is a quantum-resistant key-exchange protocol proposed by Jao et al.. As the use of mobile devices increases, the deployment of ...

#### 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 ...

#### Extensions of Signed Graphs

(University of Waterloo, 2014-04-29)

Given a signed graph (G, Σ) with an embedding on a surface S, we are interested in "extending" (G, Σ) by adding edges and splitting vertices, such that the resulting graph has no embedding on S. We show (assuming 3-connectivity ...

#### Algebraic Methods for Reducibility in Nowhere-Zero Flows

(University of Waterloo, 2007-09-25)

We study reducibility for nowhere-zero flows. A reducibility proof typically consists of showing that some induced subgraphs cannot appear in a minimum counter-example to some conjecture. We derive algebraic proofs of ...

#### On the Polyhedral Lift-and-Project Rank Conjecture for the Fractional Stable Set Polytope

(University of Waterloo, 2008-01-16)

In this thesis, we study the behaviour of Lovasz and Schrijver's lift-and-project operators N and N_0 while being applied recursively to the fractional stable set polytope of a graph. We focus on two related conjectures ...

#### 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 ...

#### Cross-monotonic Cost-Sharing Methods for Network Design Games

(University of Waterloo, 2007-09-26)

In this thesis we consider some network design games that arise from common
network design problems. A network design game involves multiple players who
control nodes in a network, each of which has a personal interest ...

#### Self-Complementary Arc-Transitive Graphs and Their Imposters

(University of Waterloo, 2009-01-28)

This thesis explores two infinite families of self-complementary arc-transitive graphs: the familiar Paley graphs and the newly discovered Peisert graphs. After studying both families, we examine a result of Peisert which ...