## Search

Now showing items 1-10 of 141

#### 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 ...

#### Properties of random graphs

(University of Waterloo, 2008-09-23)

The thesis describes new results for several problems in random graph theory.
The first problem relates to the uniform random graph model in
the supercritical phase; i.e. a graph, uniformly distributed, on $n$ vertices
and ...

#### 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 ...

#### On Algorithms, Separability and Cellular Automata in Quantum Computing

(University of Waterloo, 2007-09-26)

In Part I of this thesis, we present a new model of quantum cellular automata
(QCA) based on local unitary operations. We will describe a set of desirable
properties for any QCA model, and show that all of these properties ...

#### Hardness results and approximation algorithms for some problems on graphs

(University of Waterloo, 2008-12-17)

This thesis has two parts. In the first part, we study some graph covering problems with a non-local covering rule that allows a "remote" node to be covered by repeatedly applying the covering rule. In the second part, we ...

#### Theory of measurement-based quantum computing

(University of Waterloo, 2008-12-10)

In the study of quantum computation, data is represented in terms of linear operators which form a generalized model of probability, and computations are most commonly described as products of unitary transformations, which ...

#### Negative Correlation Properties for Matroids

(University of Waterloo, 2008-12-23)

In pursuit of negatively associated measures, this thesis focuses on certain negative correlation properties in matroids. In particular, the results presented contribute to the search for matroids which satisfy
$$P(\{X:e,f\in ...

#### 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 ...

#### 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 Puzzle-Based Synthesis Algorithm For a Triple Intersection of Schubert Varieties

(University of Waterloo, 2010-01-29)

This thesis develops an algorithm for the Schubert calculus of the Grassmanian.
Specifically, we state a puzzle-based, synthesis algorithm for a triple
intersection of Schubert varieties. Our algorithm is a reformulation ...