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
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Linearly-dense classes of matroids with bounded branch-width
(University of Waterloo, 2017-09-27)Let $M$ be a non-empty minor-closed class of matroids with bounded branch-width that does not contain arbitrarily large simple rank-$2$ matroids. For each non-negative integer $n$ we denote by $ex(n)$ the size of the ... -
Combinatorial Arithmetic on Elliptic Curves
(University of Waterloo, 2017-09-27)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, 2017-09-20)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 post-quantum digital signature scheme based on supersingular isogenies
(University of Waterloo, 2017-09-20)We present the first general-purpose 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, 2017-08-31)In this thesis we present a self-contained 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 excluded-minor characterization ... -
A quadratic programming approach to find faces in robust nonnegative matrix factorization
(University of Waterloo, 2017-08-29)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, 2017-08-29)An edge-weighted graph G = (V,E) is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in some interesting game theory ... -
Some Upper and Lower Bounds regarding Query Complexity
(University of Waterloo, 2017-08-29)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, 2017-08-29)There has been significant research about cascade effects that occur when information is spread through a network. Most models of such cascade effects are highly-localised, which means that they assume a node’s behaviour ... -
Generating Functions for Hyperbolic Plane Tessellations
(University of Waterloo, 2017-08-28)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 Domain-Driven Barriers and Primal-Dual Interior-Point Methods
(University of Waterloo, 2017-08-24)This thesis studies the theory and implementation of infeasible-start primal-dual interior-point methods for convex optimization problems. Convex optimization has applications in many fields of engineering and science such ... -
Computing with Multi-Row Intersection Cuts
(University of Waterloo, 2017-05-16)Cutting planes are one of the main techniques currently used to solve large-scale Mixed-Integer Linear Programming (MIP) models. Many important cuts used in practice, such as Gomory Mixed-Integer (GMI) cuts, are obtained ... -
Approximating Minimum-Size 2-Edge-Connected and 2-Vertex-Connected Spanning Subgraphs
(University of Waterloo, 2017-04-27)We study the unweighted 2-edge-connected and 2-vertex-connected spanning subgraph problems. A graph is 2-edge-connected if it is connected on removal of an edge, and it is 2-vertex-connected if it is connected on removal ... -
Primal Cutting Plane Methods for the Traveling Salesman Problem
(University of Waterloo, 2017-04-26)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 Random-Oracle Model
(University of Waterloo, 2017-04-25)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, 2017-04-19)Cryptographers and security experts around the world have been awakened to the reality that one day (potentially soon) large-scale quantum computers may be available. Most of the public-key cryptosystems employed today on ... -
Approximation Algorithms for Clustering and Facility Location Problems
(University of Waterloo, 2017-04-06)Facility location problems arise in a wide range of applications such as plant or warehouse location problems, cache placement problems, and network design problems, and have been widely studied in Computer Science and ... -
Efficient Composition of Discrete Time Quantum Walks
(University of Waterloo, 2017-01-20)It is well known that certain search problems are efficiently solved by quantum walk algorithms. Of particular interest are those problems whose efficient solutions involve nesting of search algorithms. The nesting of ... -
On The Density of Binary Matroids Without a Given Minor
(University of Waterloo, 2016-12-21)This thesis is motivated by the following question: how many elements can a simple binary matroid with no $\PG(t,2)$-minor have? This is a natural analogue of questions asked about the density of graphs in minor-closed ... -
Structure in Stable Matching Problems
(University of Waterloo, 2016-12-14)In this thesis we provide two contributions to the study of structure in stable matching problems. The first contribution is a short new proof for the integrality of Rothblum’s linear description of the convex hull of ...
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