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Now showing items 1-10 of 99

#### 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 ...

#### 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 ...

#### Approximation Algorithms for Path TSP, ATSP, and TAP via Relaxations

(University of Waterloo, 2015-07-29)

Linear programming (LP) relaxations provide a powerful technique to design approximation algorithms for combinatorial optimization problems. In the first part of the thesis, we study the metric s-t path Traveling Salesman ...

#### Connectivity, tree-decompositions and unavoidable-minors

(University of Waterloo, 2015-05-06)

The results in this thesis are steps toward bridging the gap between the handful of exact structure theorems known for minor-closed classes of graphs, and the very general, yet wildly qualitative, Graph Minors Structure ...

#### Matchings and games on networks

(University of Waterloo, 2015-08-20)

We investigate computational aspects of popular solution concepts for different models of network games. In chapter 3 we study balanced solutions for network bargaining games with general capacities, where agents can ...

#### 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 ...

#### 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 ...

#### 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, ...

#### 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 ...

#### 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. ...