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Now showing items 1-10 of 62

#### 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 ...

#### The Cycling Property for the Clutter of Odd st-Walks

(University of Waterloo, 2014-01-23)

A binary clutter is cycling if its packing and covering linear program have integral optimal solutions for all Eulerian edge capacities. We prove that the clutter of odd st- walks of a signed graph is cycling if and only ...

#### 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 ...

#### Signing with Codes

(University of Waterloo, 2014-01-22)

Code-based cryptography is an area of classical cryptography in which cryptographic primitives rely on hard problems and trapdoor functions related to linear error-correcting codes. Since its inception in 1978, the area ...

#### Entropy and Graphs

(University of Waterloo, 2014-01-23)

The entropy of a graph is a functional depending both on the graph itself and on a probability distribution on its vertex set. This graph functional originated from the problem of source coding in information theory and ...

#### On the Integrality Gap of Directed Steiner Tree Problem

(University of Waterloo, 2014-05-27)

In the Directed Steiner Tree problem, we are given a directed graph G = (V,E) with edge costs, a root vertex r ∈ V, and a terminal set X ⊆ V . The goal is to find the cheapest subset of edges that contains an r-t path for ...

#### The Master Equality Polyhedron: Two-Slope Facets and Separation Algorithm

(University of Waterloo, 2015-08-11)

This thesis presents our findings about the Master Equality Polyhedron (MEP), an extension of Gomory's Master Group Polyhedron. We prove a theorem analogous to Gomory and Johnson's two-slope theorem for the case of the ...

#### Combinatorial aspects of braids with applications to cryptography

(University of Waterloo, 2015-08-25)

This thesis is a collection of different results on braids, and draws connections between them. We first introduce braids by showcasing a number of equivalent ways of describing what a braid is, and how those representations ...

#### 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 ...

#### The Number Field Sieve for Barreto-Naehrig Curves: Smoothness of Norms

(University of Waterloo, 2015-05-20)

The security of pairing-based cryptography can be reduced to the difficulty of the discrete logarithm problem (DLP) in finite fields of medium characteristic. The number field sieve is the best known algorithm for this ...