Combinatorics and Optimization
This is the collection for the University of Waterloo's Department of Combinatorics and Optimization .
Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).
Waterloo faculty, students, and staff can contact us or visit the UWSpace guide to learn more about depositing their research.
Recent deposits

On Geometric Drawings of Graphs
(University of Waterloo, 20180418)This thesis is about geometric drawings of graphs and their topological generalizations. First, we study pseudolinear drawings of graphs in the plane. A pseudolinear drawing is one in which every edge can be extended ... 
A Primal Dual Algorithm On 2Steiner Graphs
(University of Waterloo, 20180123)The Steiner Tree Problem is a fundamental network design problem, where the goal is to connect a subset of terminals of a given network at minimum cost. A major open question regarding this problem, is proving that the ... 
5Choosability of Planarplustwoedge Graphs
(University of Waterloo, 20180102)We prove that graphs that can be made planar by deleting two edges are 5choosable. To arrive at this, first we prove an extension of a theorem of Thomassen. Second, we prove an extension of a theorem Postle and Thomas. ... 
Extending Pappus' Theorem
(University of Waterloo, 20171222)Let $M_1$ and $M_2$ be matroids such that $M_2$ arises from $M_1$ by relaxing a circuithyperplane. We will prove that if $M_1$ and $M_2$ are both representable over some finite field $GF(q)$, then $M_1$ and $M_2$ have ... 
Linearlydense classes of matroids with bounded branchwidth
(University of Waterloo, 20170927)Let $M$ be a nonempty minorclosed class of matroids with bounded branchwidth that does not contain arbitrarily large simple rank$2$ matroids. For each nonnegative integer $n$ we denote by $ex(n)$ the size of the ... 
Combinatorial Arithmetic on Elliptic Curves
(University of Waterloo, 20170927)We propose a scalar multiplication technique on an elliptic curve, which operates on triples of collinear points. The computation of this operation requires a new approach to operation chains, with similarities to Montgomery ... 
On The Circuit Diameters of Some Combinatorial Polytopes
(University of Waterloo, 20170920)The combinatorial diameter of a polytope P is the maximum value of a shortest path between two vertices of P, where the path uses the edges of P only. In contrast to the combinatorial diameter, the circuit diameter of P ... 
A postquantum digital signature scheme based on supersingular isogenies
(University of Waterloo, 20170920)We present the first generalpurpose digital signature scheme based on supersingular elliptic curve isogenies secure against quantum adversaries in the quantum random oracle model with small key sizes. This scheme is ... 
Circle Graph Obstructions
(University of Waterloo, 20170831)In this thesis we present a selfcontained proof of Bouchet’s characterization of the class of circle graphs. The proof uses signed graphs and is analogous to Gerards’ graphic proof of Tutte’s excludedminor characterization ... 
A quadratic programming approach to find faces in robust nonnegative matrix factorization
(University of Waterloo, 20170829)Nonnegative matrix factorization (NMF) is a popular dimensionality reduction technique because it is easily interpretable and can discern useful features. For a given matrix M (dimension n x m) whose entries are nonnegative ... 
Stabilizing Weighted Graphs
(University of Waterloo, 20170829)An edgeweighted graph G = (V,E) is called stable if the value of a maximumweight matching equals the value of a maximumweight fractional matching. Stable graphs play an important role in some interesting game theory ... 
Some Upper and Lower Bounds regarding Query Complexity
(University of Waterloo, 20170829)Query complexity is one of the several notions of complexity de ned to measure the cost of algorithms. It plays an important role in demonstrating the quantum advantage, that quantum computing is faster than classical ... 
Technology Diffusion on Spiders
(University of Waterloo, 20170829)There has been significant research about cascade effects that occur when information is spread through a network. Most models of such cascade effects are highlylocalised, which means that they assume a node’s behaviour ... 
Generating Functions for Hyperbolic Plane Tessellations
(University of Waterloo, 20170828)For a hyperbolic plane tessellation there is a generating function with respect to the distance. This generating function is the same as the growth function of a group of isometries of hyperbolic plane that acts regularly ... 
Convex Optimization via DomainDriven Barriers and PrimalDual InteriorPoint Methods
(University of Waterloo, 20170824)This thesis studies the theory and implementation of infeasiblestart primaldual interiorpoint methods for convex optimization problems. Convex optimization has applications in many fields of engineering and science such ... 
Computing with MultiRow Intersection Cuts
(University of Waterloo, 20170516)Cutting planes are one of the main techniques currently used to solve largescale MixedInteger Linear Programming (MIP) models. Many important cuts used in practice, such as Gomory MixedInteger (GMI) cuts, are obtained ... 
Approximating MinimumSize 2EdgeConnected and 2VertexConnected Spanning Subgraphs
(University of Waterloo, 20170427)We study the unweighted 2edgeconnected and 2vertexconnected spanning subgraph problems. A graph is 2edgeconnected if it is connected on removal of an edge, and it is 2vertexconnected if it is connected on removal ... 
Primal Cutting Plane Methods for the Traveling Salesman Problem
(University of Waterloo, 20170426)Most serious attempts at solving the traveling salesman problem (TSP) are based on the dual fractional cutting plane approach, which moves from one lower bound to the next. This thesis describes methods for implementing ... 
Signature Schemes in the Quantum RandomOracle Model
(University of Waterloo, 20170425)A signature scheme is a fundamental component in modern digital communication. It allows for authenticated messages, without which it would be nearly impossible to ensure security when using most modern technologies. ... 
Digital Signature Schemes Based on Hash Functions
(University of Waterloo, 20170419)Cryptographers and security experts around the world have been awakened to the reality that one day (potentially soon) largescale quantum computers may be available. Most of the publickey cryptosystems employed today on ...