Browsing Combinatorics and Optimization by Title
Now showing items 76-95 of 436
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The combinatorics of the Jack parameter and the genus series for topological maps
(University of Waterloo, 2009-08-19)Informally, a rooted map is a topologically pointed embedding of a graph in a surface. This thesis examines two problems in the enumerative theory of rooted maps. The b-Conjecture, due to Goulden and Jackson, predicts ... -
Communication Complexity of Remote State Preparation
(University of Waterloo, 2014-05-27)Superdense coding and quantum teleportation are two phenomena which were not possible without prior entanglement. In superdense coding, one sends n bits of information using n/2 qubits in the presence of shared entanglement. ... -
Comparing Classical Portfolio Optimization and Robust Portfolio Optimization on Black Swan Events
(University of Waterloo, 2021-01-29)Black swan events, such as natural catastrophes and manmade market crashes, historically have a drastic negative influence on investments; and there is a discrepancy on losses caused by these two types of disasters. In ... -
Comparing Intersection Cut Closures using Simple Families of Lattice-Free Convex Sets
(University of Waterloo, 2022-04-26)Mixed integer programs are a powerful mathematical tool, providing a general model for expressing both theoretically difficult and practically useful problems. One important subroutine of algorithms solving mixed integer ... -
A Complete Multipartite Basis for the Chromatic Symmetric Function
(Society for Industrial and Applied Mathematics, 2021-11-15)In the vector space of symmetric functions, the elements of the basis of elementary symmetric functions are (up to a factor) the chromatic symmetric functions of disjoint unions of cliques. We consider their graph complements, ... -
Complexity Dichotomy for List-5-Coloring with a Forbidden Induced Subgraph
(Society for Industrial and Applied Mathematics, 2022-08-30)For a positive integer r and graphs G and H, we denote by G+H the disjoint union of G and H and by rH the union of r mutually disjoint copies of H. Also, we say G is H-free if H is not isomorphic to an induced subgraph of ... -
Complexity of Ck-Coloring in Hereditary Classes of Graphs
(Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2019)For a graph F, a graph G is F-free if it does not contain an induced subgraph isomorphic to F. For two graphs G and H, an H-coloring of G is a mapping f : V (G) --> V (H) such that for every edge uv E(G) it holds that ... -
The complexity of some set-partitioning formulations for the vehicle routing problem with stochastic demands
(University of Waterloo, 2020-10-28)The capacitated vehicle routing problem with stochastic demands (CVRPSD) is a variant of the deterministic capacitated vehicle routing problem (CVRP). The CVRP consists of planning routes for vehicles with a given capacity ... -
A Comprehensive Analysis of Lift-and-Project Methods for Combinatorial Optimization
(University of Waterloo, 2014-08-20)In both mathematical research and real-life, we often encounter problems that can be framed as finding the best solution among a collection of discrete choices. Many of these problems, on which an exhaustive search in the ... -
A computational study of practical issues arising in short-term scheduling of a multipurpose facility
(University of Waterloo, 2019-01-23)This thesis focuses on two important considerations when solving short term scheduling problems for multipurpose facilities: deciding when rescheduling should be performed and choosing efficient time representations for ... -
Computing the Nucleolus of Matching and b-Matching Games
(University of Waterloo, 2021-05-21)In the classical weighted matching problem the optimizer is given a graph with edge weights and their goal is to find a matching which maximizes the sum of the weights of edges in the matching. It is typically assumed in ... -
Computing the Residue Class of Partition Numbers
(University of Waterloo, 2016-09-14)In 1919, Ramanujan initiated the study of congruence properties of the integer partition function $p(n)$ by showing that $$p(5n+4) \equiv 0 \mod{5}$$ and $$p(7n+5) \equiv 0 \mod{7}$$ hold for all integers $n$. These results ... -
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 ... -
Concatenating Bipartite Graphs
(The Electronic Journal of Combinatorics, 2022)Let x, y E (0, 1], and let A, B, C be disjoint nonempty stable subsets of a graph G, where every vertex in A has at least x |B| neighbors in B, and every vertex in B has at least y|C| neighbors in C, and there are no edges ... -
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 ... -
Constructing Cospectral and Comatching Graphs
(University of Waterloo, 2019-07-18)The matching polynomial is a graph polynomial that does not only have interesting mathematical properties, but also possesses meaningful applications in physics and chemistry. For a simple graph, the matching polynomial ... -
Continuous-time Quantum Algorithms: Searching and Adiabatic Computation
(University of Waterloo, 2002)One of the most important quantum algorithms is Grover's search algorithm [G96]. Quantum searching can be used to speed up the search for solutions to NP-complete problems e. g. 3SAT. Even so, the best known quantum ... -
Contributions at the Interface Between Algebra and Graph Theory
(University of Waterloo, 2013-01-07)In this thesis, we make some contributions at the interface between algebra and graph theory. In Chapter 1, we give an overview of the topics and also the definitions and preliminaries. In Chapter 2, we estimate the ... -
Convergence Analysis of Generalized Primal-Dual Interior-Point Algorithms for Linear Optimization
(University of Waterloo, 2002)We study the zeroth-, first-, and second-order algorithms proposed by Tuncel. The zeroth-order algorithms are the generalization of the classic primal-dual affine-scaling methods, and have a strong connection with the ... -
Convex Algebraic Geometry Approaches to Graph Coloring and Stable Set Problems
(University of Waterloo, 2021-08-23)The objective of a combinatorial optimization problem is to find an element that maximizes a given function defined over a large and possibly high-dimensional finite set. It is often the case that the set is so large that ...