Browsing Mathematics (Faculty of) by Subject "graph"
Now showing items 1-12 of 12
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A+ Indexes: Highly Flexible Adjacency Lists in Graph Database Management Systems
(University of Waterloo, 2019-09-17)Adjacency lists are the most fundamental storage structure in existing graph database management systems (GDBMSs) to index input graphs. Adjacency lists are universally linked-list like per-vertex structures that allow ... -
The Algebraic Kirchberg--Phillips Conjecture for Leavitt Path Algebras
(University of Waterloo, 2015-09-18)This essay is meant to be an exposition of the theory of Leavitt path algebras and graph C*-algebras, with an aim to discuss some current classification questions. These two classes of algebras sit on opposite sides of a ... -
BotChase: Graph-Based Bot Detection Using Machine Learning
(University of Waterloo, 2019-05-21)Bot detection using machine learning (ML), with network flow-level features, has been extensively studied in the literature. However, existing flow-based approaches typically incur a high computational overhead and do not ... -
Edge-disjoint Linkages in Infinite Graphs
(University of Waterloo, 2022-09-26)The main subject of this thesis is the infinite graph version of the weak linkage conjecture by Thomassen [24]. We first prove results about the structure of the lifting graph; Theorems 2.2.8, 2.2.24, and 2.3.1. As an ... -
A Fundamentally Topological Perspective on Graph Theory
(University of Waterloo, 2005)We adopt a novel topological approach for graphs, in which edges are modelled as points as opposed to arcs. The model of classical <i>topologized graphs</i> translates graph isomorphism into topological homeomorphism, ... -
Graph-Based Spatial-Temporal Cluster Evolution: Representation, Analysis, and Implementation
(University of Waterloo, 2023-08-28)Spatial-temporal data are information about real-world entities that exist in a location, the spatial dimension, and during a period of time, the temporal dimension. These real-world entities, such as vehicles, people, or ... -
On Geometric Drawings of Graphs
(University of Waterloo, 2018-04-18)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 ... -
On the Crossing Numbers of Complete Graphs
(University of Waterloo, 2006)In this thesis we prove two main results. The Triangle Conjecture asserts that the convex hull of any optimal rectilinear drawing of <em>K<sub>n</sub></em> must be a triangle (for <em>n</em> ≥ 3). We prove that, ... -
Succinct Indexes
(University of Waterloo, 2008-02-14)This thesis defines and designs succinct indexes for several abstract data types (ADTs). The concept is to design auxiliary data structures that ideally occupy asymptotically less space than the information-theoretic lower ... -
Transitive Factorizations of Permutations and Eulerian Maps in the Plane
(University of Waterloo, 2005)The problem of counting ramified covers of a Riemann surface up to homeomorphism was proposed by Hurwitz in the late 1800's. This problem translates combinatorially into factoring a permutation with a specified cycle ... -
Uniqueness and Complexity in Generalised Colouring
(University of Waterloo, 2003)The study and recognition of graph families (or graph properties) is an essential part of combinatorics. Graph colouring is another fundamental concept of graph theory that can be looked at, in large part, as the recognition ... -
Updating the Vertex Separation of a Dynamically Changing Tree
(University of Waterloo, 2004)This thesis presents several algorithms that update the vertex separation of a tree after the tree is modified; the vertex separation of a graph measures the largest number of vertices to the left of and including a vertex ...