## Search

Now showing items 1-10 of 22

#### Morphing planar triangulations

(University of Waterloo, 2014-06-09)

A morph between two drawings of the same graph can be thought of as a continuous deformation between the two given drawings. A morph is linear if every vertex moves along a straight line segment from its initial position ...

#### On the Relationship between Conjugate Gradient and Optimal First-Order Methods for Convex Optimization

(University of Waterloo, 2014-01-23)

In a series of work initiated by Nemirovsky and Yudin, and later extended by Nesterov, first-order algorithms for unconstrained minimization with optimal theoretical complexity bound have been proposed. On the other hand, ...

#### Mechanism Design For Covering Problems

(University of Waterloo, 2014-01-24)

Algorithmic mechanism design deals with efficiently-computable algorithmic constructions in the presence of strategic players who hold the inputs to the problem and may misreport their input if doing so benefits them. ...

#### 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 ...

#### 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 Local Chromatic Number

(University of Waterloo, 2014-01-23)

A graph vertex colouring is called k-local if the number of colours used in the closed neighbourhood of each vertex is at most k. The local chromatic number of a graph is the smallest k for which the graph has a proper ...

#### A Comprehensive Analysis of Lift-and-Project Methods for Combinatorial Optimization

(University of Waterloo, 2014-08-20)

In both mathematical research and real-life, we often encounter problems that can be framed as finding the best solution among a collection of discrete choices. Many of these problems, on which an exhaustive search in the ...

#### Efficient Jacobian Determination by Structure-Revealing Automatic Differentiation

(University of Waterloo, 2014-01-23)

This thesis is concerned with the efficient computation of Jacobian matrices of nonlinear
vector maps using automatic differentiation (AD). Specifically, we propose the use of
two directed edge separator methods, the ...