Browsing Combinatorics and Optimization by Title
Now showing items 73-92 of 436
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Combinatorially Thin Trees and Spectrally Thin Trees in Structured Graphs
(University of Waterloo, 2023-12-19)Given a graph $G=(V,E)$, finding simpler estimates of $G$ with possibly fewer edges or vertices while capturing some of its specific properties has been used in order to design efficient algorithms. The concept of estimating ... -
Combinatorics and the KP Hierarchy
(University of Waterloo, 2009-10-01)The study of the infinite (countable) family of partial differential equations known as the Kadomtzev - Petviashvili (KP) hierarchy has received much interest in the mathematical and theoretical physics community for ... -
Combinatorics of Grassmannian Decompositions
(University of Waterloo, 2019-08-22)This thesis studies several combinatorially defined families of subsets of the Grassmannian. We introduce and study a family of subsets called “basis shape loci” associated to transversal matroids. Additionally, we study ... -
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 ...