## Search

Now showing items 1-10 of 21

#### On primal-dual interior-point algorithms for convex optimisation

(2015-09-25)

This thesis studies the theory and implementation of interior-point methods
for convex optimisation. A number of important problems from mathematics and
engineering can be cast naturally as convex optimisation ...

#### Enumerative Applications of Integrable Hierarchies

(University of Waterloo, 2015-05-21)

Countably infinite families of partial differential equations such as the Kadomtzev - Petviashvili (KP) hierarchy and the B-type KP (BKP) hierarchy have received much interest in the mathematical and theoretical physics ...

#### Approximation Algorithms for Graph Protection Problems

(University of Waterloo, 2015-05-22)

We study a budgeted cut problem known as Graph Protection, where
the goal is to remove edges of a given graph in order to protect
valuable nodes from stochastic, infectious threats. This problem was
recently proposed ...

#### Combinatorial Algorithms for Submodular Function Minimization and Related Problems

(University of Waterloo, 2015-05-19)

Submodular functions are common in combinatorics; examples include the cut capacity function of a graph and the rank function of a matroid. The submodular function minimization problem generalizes the classical minimum cut ...

#### 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 ...

#### Finding a Second Hamiltonian cycle in Barnette Graphs

(University of Waterloo, 2015-08-31)

We study the following two problems: (1) finding a second room-partitioning of an oik, and (2) finding a second Hamiltonian cycle in cubic graphs. The existence of solution for both problems is guaranteed by a parity ...

#### Rayleigh Property of Lattice Path Matroids

(University of Waterloo, 2015-09-22)

In this work, we studied the class of lattice path matroids $\mathcal{L}$, which was first introduced by J.E. Bonin. A.D. Mier, and M. Noy in [\ref{Bonin 2002}]. Lattice path matroids are transversal, and $\mathcal{L}$ is ...

#### 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 ...

#### 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 ...