Browsing Combinatorics and Optimization by Title
Now showing items 133-152 of 436
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Dominating sets in Kneser graphs
(University of Waterloo, 2007-08-29)This thesis investigates dominating sets in Kneser graphs as well as a selection of other topics related to graph domination. Dominating sets in Kneser graphs, especially those of minimum size, often correspond to interesting ... -
Dynamic Pricing Schemes in Combinatorial Markets
(University of Waterloo, 2023-05-01)In combinatorial markets where buyers are self-interested, the buyers may make purchases that lead to suboptimal item allocations. As a central coordinator, our goal is to impose prices on the items of the market so that ... -
Dynamic Programming: Salesman to Surgeon
(University of Waterloo, 2013-05-15)Dynamic Programming is an optimization technique used in computer science and mathematics. Introduced in the 1950s, it has been applied to many classic combinatorial optimization problems, such as the Shortest Path Problem, ... -
Edge coloring multigraphs without small dense subsets
(Elsevier, 2015-12-06)One consequence of a long-standing conjecture of Goldberg and Seymour about the chromatic index of multigraphs would be the following statement. Suppose $G$ is a multigraph with maximum degree $\Delta$, such that no vertex ... -
Edge State Transfer
(University of Waterloo, 2019-01-11)Let G be a graph and let t be a positive real number. Then the evolution of the continuous quantum walk defined on G is described by the transition matrix U(t)=exp(itH).The matrix H is called Hamiltonian. So far the most ... -
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 ... -
The Edmonds-Giles Conjecture and its Relaxations
(University of Waterloo, 2022-12-23)Given a directed graph, a directed cut is a cut with all arcs oriented in the same direction, and a directed join is a set of arcs which intersects every directed cut at least once. Edmonds and Giles conjectured for all ... -
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 ... -
Efficient Integer Representations for Cryptographic Operations
(University of Waterloo, 2004)Every positive integer has a unique radix 2 representation which uses the digits {0,1}. However, if we allow digits other than 0 and 1, say {0,1,-1}, then a positive integer has many representations. Of these ... -
Efficient Jacobian Determination by Structure-Revealing Automatic Differentiation
(University of Waterloo, 2014-01-23)This thesis is concerned with the efficient computation of Jacobian matrices of nonlinear vector maps using automatic differentiation (AD). Specifically, we propose the use of two directed edge separator methods, the ... -
Efficient Pairings on Various Platforms
(University of Waterloo, 2012-05-14)Pairings have found a range of applications in many areas of cryptography. As such, to utilize the enormous potential of pairing-based protocols one needs to efficiently compute pairings across various computing platforms. ... -
Efficient Trust Region Subproblem Algorithms
(University of Waterloo, 2011-09-29)The Trust Region Subproblem (TRS) is the problem of minimizing a quadratic (possibly non-convex) function over a sphere. It is the main step of the trust region method for unconstrained optimization problems. Two cases may ... -
Ehrhart Theory and Unimodular Decompositions of Lattice Polytopes
(University of Waterloo, 2015-01-20)Ehrhart theory studies the behaviour of lattice points contained in dilates of lattice polytopes. We provide an introduction to Ehrhart theory. In particular, we prove Ehrhart's Theorem, Stanley Non-negativity, and ... -
Eigenvalue, Quadratic Programming and Semidefinite Programming Bounds for Graph Partitioning Problems
(University of Waterloo, 2014-09-03)The Graph Partitioning problems are hard combinatorial optimization problems. We are interested in both lower bounds and upper bounds. We introduce several methods including basic eigenvalue and projected eigenvalue ... -
Entropic Matroids and Their Representation
(Multidisciplinary Digital Publishing Institute, 2019)This paper investigates entropic matroids, that is, matroids whose rank function is given as the Shannon entropy of random variables. In particular, we consider p-entropic matroids, for which the random variables each have ... -
Entropy and Graphs
(University of Waterloo, 2014-01-23)The entropy of a graph is a functional depending both on the graph itself and on a probability distribution on its vertex set. This graph functional originated from the problem of source coding in information theory and ... -
Enumerating matroid extensions
(University of Waterloo, 2023-09-01)This thesis investigates the problem of enumerating the extensions of certain matroids. A matroid M is an extension of a matroid N if M delete e is equal to N for some element e of M. Similarly, a matroid M is a coextension ... -
Enumeration of Factorizations in the Symmetric Group: From Centrality to Non-centrality
(University of Waterloo, 2011-04-25)The character theory of the symmetric group is a powerful method of studying enu- merative questions about factorizations of permutations, which arise in areas including topology, geometry, and mathematical physics. This ... -
Enumerative Applications of Integrable Hierarchies
(University of Waterloo, 2015-05-21)Countably infinite families of partial differential equations such as the Kadomtzev - Petviashvili (KP) hierarchy and the B-type KP (BKP) hierarchy have received much interest in the mathematical and theoretical physics ... -
Enumerative perspectives on chord diagrams
(University of Waterloo, 2022-10-07)The topic of this thesis is enumerating certain classes of chord diagrams, perfect matchings of the interval $\{1, 2, \ldots, 2n\}$. We consider hereditary classes of chord diagrams that are restricted to satisfy one of ...