## Search

Now showing items 1-10 of 11

#### 2-crossing critical graphs with a V8 minor

(University of Waterloo, 2012-01-17)

The crossing number of a graph is the minimum number of pairwise crossings of edges among all planar drawings of the graph. A graph G is k-crossing critical if it has crossing number k and any proper subgraph of G has a ...

#### Cyclic Sieving Phenomenon of Promotion on Rectangular Tableaux

(University of Waterloo, 2012-09-28)

Cyclic sieving phenomenon (CSP) is a generalization by Reiner, Stanton, White of Stembridge's q=-1 phenomenon. When CSP is exhibited, orbits of a cyclic action on combinatorial objects show a nice structure and their sizes ...

#### Quantum algorithms for searching, resampling, and hidden shift problems

(University of Waterloo, 2012-09-21)

This thesis is on quantum algorithms. It has three main themes:
(1) quantum walk based search algorithms,
(2) quantum rejection sampling, and
(3) the Boolean function hidden shift problem.
The first two parts deal with ...

#### Algebraic Aspects of Multi-Particle Quantum Walks

(University of Waterloo, 2012-12-04)

A continuous time quantum walk consists of a particle moving among the vertices of a graph G. Its movement is governed by the structure of the graph. More formally, the adjacency matrix A is the Hamiltonian that determines ...

#### 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 ...

#### Highly Non-Convex Crossing Sequences

(University of Waterloo, 2012-05-18)

For a given graph, G, the crossing number crₐ(G) denotes the minimum number of edge crossings when a graph is drawn on an orientable surface of genus a. The sequence cr₀(G), cr₁(G), ... is said to be the crossing sequence ...

#### On the Security of Leakage Resilient Public Key Cryptography

(University of Waterloo, 2012-04-30)

Side channel attacks, where an attacker learns some physical information about the state of a device, are one of the ways in which cryptographic schemes are broken in practice. "Provably secure" schemes are subject to these ...

#### Efficient Pairings on Various Platforms

(University of Waterloo, 2012-05-14)

Pairings have found a range of applications in many areas of cryptography. As such, to
utilize the enormous potential of pairing-based protocols one needs to efficiently compute
pairings across various computing platforms. ...

#### LP-based Approximation Algorithms for the Capacitated Facility Location Problem

(University of Waterloo, 2012-05-18)

The capacitated facility location problem is a well known problem in combinatorial optimization and operations research. In it, we are given a set of clients and a set of possible facility locations. Each client has a ...

#### Algebraic Methods and Monotone Hurwitz Numbers

(University of Waterloo, 2012-09-21)

We develop algebraic methods to solve join-cut equations, which are partial differential equations that arise in the study of permutation factorizations. Using these techniques, we give a detailed study of the recently ...