Browsing Combinatorics and Optimization by Title
Now showing items 187-206 of 434
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H-colouring Pt-free graphs in subexponential time
(Elsevier, 2019-08-31)A graph is called Pt-free if it does not contain the path on t vertices as an induced subgraph. Let H be a multigraph with the property that any two distinct vertices share at most one common neighbour. We show that the ... -
Hamilton Paths in Generalized Petersen Graphs
(University of Waterloo, 2002)This thesis puts forward the conjecture that for <i>n</i> > 3<i>k</i> with <i>k</i> > 2, the generalized Petersen graph, <i>GP</i>(<i>n,k</i>) is Hamilton-laceable if <i>n</i> is even and <i>k</i> is odd, and it is ... -
Hardness results and approximation algorithms for some problems on graphs
(University of Waterloo, 2008-12-17)This thesis has two parts. In the first part, we study some graph covering problems with a non-local covering rule that allows a "remote" node to be covered by repeatedly applying the covering rule. In the second part, we ... -
Highly Non-Convex Crossing Sequences
(University of Waterloo, 2012-05-18)For a given graph, G, the crossing number crₐ(G) denotes the minimum number of edge crossings when a graph is drawn on an orientable surface of genus a. The sequence cr₀(G), cr₁(G), ... is said to be the crossing sequence ... -
Homomorphic Encryption
(University of Waterloo, 2013-01-24)In this thesis, we provide a summary of fully homomorphic encryption, and in particular, look at the BGV encryption scheme by Brakerski, Gentry, and Vaikuntanathan; as well the DGHV encryption scheme by van Dijk, Gentry, ... -
Hurwitz Trees and Tropical Geometry
(University of Waterloo, 2016-01-21)The lifting problem in algebraic geometry asks when a finite group G acting on a curve defined over characteristic p > 0 lifts to characteristic 0. One object used in the study of this problem is the Hurwitz tree, which ... -
Hyperpfaffians in Algebraic Combinatorics
(University of Waterloo, 2006)The pfaffian is a classical tool which can be regarded as a generalization of the determinant. The hyperpfaffian, which was introduced by Barvinok, generalizes the pfaffian to higher dimension. This was further ... -
Ideal Clutters
(University of Waterloo, 2018-04-24)Let E be a finite set of elements, and let C be a family of subsets of E called members. We say that C is a clutter over ground set E if no member is contained in another. The clutter C is ideal if every extreme point of ... -
Implementing the Castryck-Decru attack on SIDH with general primes
(University of Waterloo, 2024-01-09)With the rapid progress of quantum computers in recent years, efforts have been made to standardize new public-key cryptographic protocols which would be secure against them. One of the schemes in contention was Supersingular ... -
Implementing the Schoof-Elkies-Atkin Algorithm with NTL
(University of Waterloo, 2013-04-30)In elliptic curve cryptography, cryptosystems are based on an additive subgroup of an elliptic curve defined over a finite field, and the hardness of the Elliptic Curve Discrete Logarithm Problem is dependent on the order ... -
Implicit Loss of Surjectivity and Facial Reduction: Theory and Applications
(University of Waterloo, 2023-03-09)Facial reduction, pioneered by Borwein and Wolkowicz, is a preprocessing method that is commonly used to obtain strict feasibility in the reformulated, reduced constraint system. The importance of strict feasibility is ... -
Improved approximation guarantees for lower-bounded facility location problem
(University of Waterloo, 2010-09-28)We consider the lower-bounded facility location (LBFL) problem (, also known as load-balanced facility location), which is a generalization of uncapacitated facility location (UFL) problem where each open facility is ... -
Improving post-quantum cryptography through cryptanalysis
(University of Waterloo, 2020-07-15)Large quantum computers pose a threat to our public-key cryptographic infrastructure. The possible responses are: Do nothing; accept the fact that quantum computers might be used to break widely deployed protocols. Mitigate ... -
Independent Sets and Eigenspaces
(University of Waterloo, 2004)The problems we study in this thesis arise in computer science, extremal set theory and quantum computing. The first common feature of these problems is that each can be reduced to characterizing the independent sets ... -
Induced Binary Submatroids
(University of Waterloo, 2021-07-21)The notion of induced subgraphs is extensively studied in graph theory. An example is the famous Gy\'{a}rf\'{a}s-Sumner conjecture, which asserts that given a tree $T$ and a clique $K$, there exists a constant $c$ such ... -
Induced Subgraphs and Tree Decompositions III. Three-Path-Configurations and Logarithmic Treewidth.
(Advances in Combinatorics, 2022-09-09)A theta is a graph consisting of two non-adjacent vertices and three internally disjoint paths between them, each of length at least two. For a family H of graphs, we say a graph G is H-free if no induced subgraph of G is ... -
Induced subgraphs of graphs with large chromatic number. VIII. Long odd holes
(Elsevier, 2020-01)We prove a conjecture of András Gyárfás, that for all k, l, every graph with clique number at most κ and sufficiently large chromatic number has an odd hole of length at least ℓ. -
Induction Relations in the Symmetric Groups and Jucys-Murphy Elements
(University of Waterloo, 2018-08-16)Transitive factorizations faithfully encode many interesting objects. The well-known ones include ramified coverings of the sphere and hypermaps. Enumeration of specific classes of such objects have been known for quite ... -
Infinite graphs, graph-like spaces and B-matroids
(University of Waterloo, 2011-01-19)The central theme of this thesis is to prove results about infinite mathematical objects by studying the behaviour of their finite substructures. In particular, we study B-matroids, which are an infinite generalization ... -
Inner approximation of convex cones via primal-dual ellipsoidal norms
(University of Waterloo, 2016-05-13)We study ellipsoids from the point of view of approximating convex sets. Our focus is on finding largest volume ellipsoids with specified centers which are contained in certain convex cones. After reviewing the related ...