Browsing Combinatorics and Optimization by Title
Now showing items 318-337 of 436
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Polynomial bounds for chromatic number. III. Excluding a double star
(Wiley, 2022-10)A “double star” is a tree with two internal vertices. It is known that the Gyárfás-Sumner conjecture holds for double stars, that is, for every double star H, there is a function fH such that if G does not contain H as ... -
Portfolio Selection Under Nonsmooth Convex Transaction Costs
(University of Waterloo, 2006)We consider a portfolio selection problem in the presence of transaction costs. Transaction costs on each asset are assumed to be a convex function of the amount sold or bought. This function can be nondifferentiable ... -
Post-Quantum Account Recovery for Passwordless Authentication
(University of Waterloo, 2023-04-24)WebAuthn is a passwordless authentication protocol which allows users to authenticate to online services using public-key cryptography. Users prove their identity based on possession of a private key, which is stored on a ... -
A post-quantum digital signature scheme based on supersingular isogenies
(University of Waterloo, 2017-09-20)We present the first general-purpose digital signature scheme based on supersingular elliptic curve isogenies secure against quantum adversaries in the quantum random oracle model with small key sizes. This scheme is ... -
Post-Quantum Security of Authenticated Key Establishment Protocols
(University of Waterloo, 2016-04-20)We present a security model for authenticated key establishment that allows for quantum interactions between the adversary and quantum oracles that emulate classical parties, resulting in a truly post-quantum security ... -
Postman Problems on Mixed Graphs
(University of Waterloo, 2003)The <i>mixed postman problem</i> consists of finding a minimum cost tour of a mixed graph <i>M</i> = (<i>V</i>,<i>E</i>,<i>A</i>) traversing all its edges and arcs at least once. We prove that two well-known linear ... -
Practical Lattice Cryptosystems: NTRUEncrypt and NTRUMLS
(University of Waterloo, 2015-12-22)Public key cryptography, as deployed on the internet today, stands on shaky ground. For over twenty years now it has been known that the systems in widespread use are insecure against adversaries equipped with quantum ... -
Preprocessing and Reduction for Semidefinite Programming via Facial Reduction: Theory and Practice
(University of Waterloo, 2013-11-26)Semidefinite programming is a powerful modeling tool for a wide range of optimization and feasibility problems. Its prevalent use in practice relies on the fact that a (nearly) optimal solution of a semidefinite program ... -
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 ...