Browsing Combinatorics and Optimization by Title
Now showing items 325-344 of 435
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Primal Cutting Plane Methods for the Traveling Salesman Problem
(University of Waterloo, 2017-04-26)Most serious attempts at solving the traveling salesman problem (TSP) are based on the dual fractional cutting plane approach, which moves from one lower bound to the next. This thesis describes methods for implementing ... -
A Primal Dual Algorithm On 2-Steiner Graphs
(University of Waterloo, 2018-01-23)The Steiner Tree Problem is a fundamental network design problem, where the goal is to connect a subset of terminals of a given network at minimum cost. A major open question regarding this problem, is proving that the ... -
A Primer on Cryptographic Multilinear Maps and Code Obfuscation
(University of Waterloo, 2015-09-23)The construction of cryptographic multilinear maps and a general-purpose code obfuscator were two long-standing open problems in cryptography. It has been clear for a number of years that constructions of these two ... -
Probabilistic Choice Models for Product Pricing Using Reservation Prices
(University of Waterloo, 2007-01-22)The problem of pricing a product line to maximize profits is an important challenge faced by many companies. To address this problem, we discuss four different probabilistic choice models that are based on reservation ... -
Proof of the Kalai-Meshulam conjecture
(Springer Nature, 2020-07-01)Let G be a graph, and let fG be the sum of (−1)∣A∣, over all stable sets A. If G is a cycle with length divisible by three, then fG = ±2. Motivated by topological considerations, G. Kalai and R. Meshulam [8] made the ... -
Properties of graphs with large girth
(University of Waterloo, 2008-01-24)This thesis is devoted to the analysis of a class of iterative probabilistic algorithms in regular graphs, called locally greedy algorithms, which will provide bounds for graph functions in regular graphs with ... -
Properties of random graphs
(University of Waterloo, 2008-09-23)The thesis describes new results for several problems in random graph theory. The first problem relates to the uniform random graph model in the supercritical phase; i.e. a graph, uniformly distributed, on $n$ vertices and ... -
Properties of Stable Matchings
(University of Waterloo, 2010-12-17)Stable matchings were introduced in 1962 by David Gale and Lloyd Shapley to study the college admissions problem. The seminal work of Gale and Shapley has motivated hundreds of research papers and found applications in ... -
Pure Pairs VI. Excluding an Ordered Tree.
(Society for Industrial and Applied Mathematics Journal on Discrete Mathematics, 2022-01)A pure pair in a graph G is a pair (Z1,Z2) of disjoint sets of vertices such that either every vertex in Z1 is adjacent to every vertex in Z2, or there are no edges between Z1 and Z2. With Maria Chudnovsky, we recently ... -
Pure pairs. I. Trees and linear anticomplete pairs
(Elsevier, 2020-12-02)The Erdős-Hajnal conjecture asserts that for every graph H there is a constant c > 0 such that every graph G that does not contain H as an induced subgraph has a clique or stable set of cardinality at least |G|c. In this ... -
Pure pairs. II. Excluding all subdivisions of a graph
(Springer Nature, 2021-06-01)We prove for every graph H there exists ɛ > 0 such that, for every graph G with |G|≥2, if no induced subgraph of G is a subdivision of H, then either some vertex of G has at least ɛ|G| neighbours, or there are two disjoint ... -
Pure pairs. III. Sparse graphs with no polynomial-sized anticomplete pairs
(Wiley, 2020-11)A graph is H-free if it has no induced subgraph isomorphic to H, and |G| denotes the number of vertices of G. A conjecture of Conlon, Sudakov and the second author asserts that: - For every graph H, there exists ∈ > 0 ... -
A Puzzle-Based Synthesis Algorithm For a Triple Intersection of Schubert Varieties
(University of Waterloo, 2010-01-29)This thesis develops an algorithm for the Schubert calculus of the Grassmanian. Specifically, we state a puzzle-based, synthesis algorithm for a triple intersection of Schubert varieties. Our algorithm is a reformulation ... -
A quadratic programming approach to find faces in robust nonnegative matrix factorization
(University of Waterloo, 2017-08-29)Nonnegative matrix factorization (NMF) is a popular dimensionality reduction technique because it is easily interpretable and can discern useful features. For a given matrix M (dimension n x m) whose entries are nonnegative ... -
Quadratically Dense Matroids
(University of Waterloo, 2020-07-08)This thesis is concerned with finding the maximum density of rank-$n$ matroids in a minor-closed class. The extremal function of a non-empty minor-closed class $\mathcal M$ of matroids which excludes a rank-2 uniform ... -
Quantum algorithms for searching, resampling, and hidden shift problems
(University of Waterloo, 2012-09-21)This thesis is on quantum algorithms. It has three main themes: (1) quantum walk based search algorithms, (2) quantum rejection sampling, and (3) the Boolean function hidden shift problem. The first two parts deal with ... -
Quantum Compression and Quantum Learning via Information Theory
(University of Waterloo, 2020-12-21)This thesis consists of two parts: quantum compression and quantum learning theory. A common theme between these problems is that we study them through the lens of information theory. We first study the task of visible ... -
Quantum Cost Models for Cryptanalysis of Isogenies
(University of Waterloo, 2019-05-01)Isogeny-based cryptography uses keys large enough to resist a far-future attack from Tani’s algorithm, a quantum random walk on Johnson graphs. The key size is based on an analysis in the query model. Queries do not ... -
Quantum independence and chromatic numbers
(University of Waterloo, 2019-08-28)In this thesis we are studying the cases when quantum independence and quantum chromatic numbers coincide with or differ from their classical counterparts. Knowing about the relation of chromatic numbers separation to the ... -
Quantum Information Processing with Adversarial Devices
(University of Waterloo, 2010-06-09)We consider several applications in black-box quantum computation in which untrusted physical quantum devices are connected together to produce an experiment. By examining the outcome statistics of such an experiment, and ...