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Now showing items 1-10 of 15

#### 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 ...

#### Node-Weighted Prize Collecting Steiner Tree and Applications

(University of Waterloo, 2013-05-23)

The Steiner Tree problem has appeared in the Karp's list of the first 21 NP-hard problems and is well known as one of the most fundamental problems in Network Design area. We study the Node-Weighted version of the Prize ...

#### Single Commodity Flow Algorithms for Lifts of Graphic and Cographic Matroids

(University of Waterloo, 2013-01-23)

Consider a binary matroid M given by its matrix representation. We show that if M is a lift of a graphic or a cographic matroid, then in polynomial time we can either solve the single commodity flow problem for M or find ...

#### Preprocessing and Reduction for Semidefinite Programming via Facial Reduction: Theory and Practice

(University of Waterloo, 2013-11-26)

Semidefinite programming is a powerful modeling tool for a wide range of optimization and feasibility problems. Its prevalent use in practice relies on the fact that a (nearly) optimal solution of a semidefinite program ...

#### Homomorphic Encryption

(University of Waterloo, 2013-01-24)

In this thesis, we provide a summary of fully homomorphic encryption, and in particular, look at the BGV encryption scheme by Brakerski, Gentry, and Vaikuntanathan; as well the DGHV encryption scheme by van Dijk, Gentry, ...

#### Dynamic Programming: Salesman to Surgeon

(University of Waterloo, 2013-05-15)

Dynamic Programming is an optimization technique used in computer science and mathematics. Introduced in the 1950s, it has been applied to many classic combinatorial optimization problems, such as the Shortest Path Problem, ...

#### Core Structures in Random Graphs and Hypergraphs

(University of Waterloo, 2013-08-30)

The k-core of a graph is its maximal subgraph with minimum degree at least k. The study of k-cores in random graphs was initiated by Bollobás in 1984 in connection to k-connected subgraphs of random graphs. Subsequently, ...

#### Implementing the Schoof-Elkies-Atkin Algorithm with NTL

(University of Waterloo, 2013-04-30)

In elliptic curve cryptography, cryptosystems are based on an additive subgroup of an elliptic curve defined over a finite field, and the hardness of the Elliptic Curve Discrete Logarithm Problem is dependent on the order ...

#### Transmitting Quantum Information Reliably across Various Quantum Channels

(University of Waterloo, 2013-05-01)

Transmitting quantum information across quantum channels is an important task. However quantum information is delicate, and is easily corrupted. We address the task of protecting quantum information from an information ...

#### A Quick-and-Dirty Approach to Robustness in Linear Optimization

(University of Waterloo, 2013-01-07)

We introduce methods for dealing with linear programming (LP) problems
with uncertain data, using the notion of weighted analytic centers.
Our methods are based on high interaction with the decision maker (DM) and try ...