Browsing Combinatorics and Optimization by Title
Now showing items 394-413 of 435
-
Split Cuts From Sparse Disjunctions
(University of Waterloo, 2019-01-16)Cutting planes are one of the major techniques used in solving Mixed-Integer Linear Programming (MIP) models. Various types of cuts have long been exploited by MIP solvers, leading to state-of-the-art performance in practice. ... -
A Stability Theorem for Matchings in Tripartite 3-Graphs
(Cambridge University Press, 2018-04-02)It follows from known results that every regular tripartite hypergraph of positive degree, with n vertices in each class, has matching number at least n/2. This bound is best possible, and the extremal configuration is ... -
Stabilizing Weighted Graphs
(University of Waterloo, 2017-08-29)An edge-weighted graph G = (V,E) is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in some interesting game theory ... -
State Transfer & Strong Cospectrality in Cayley Graphs
(University of Waterloo, 2022-08-09)This thesis is a study of two graph properties that arise from quantum walks: strong cospectrality of vertices and perfect state transfer. We prove various results about these properties in Cayley graphs. We consider ... -
Stochastic Minimum Norm Combinatorial Optimization
(University of Waterloo, 2022-07-28)Motivated by growing interest in optimization under uncertainty, we undertake a systematic study of designing approximation algorithms for a wide class of 1-stage stochastic-optimization problems with norm-based objective ... -
STPA-Sec Applied to Path Planning: Quantum-Safe Autonomous Vehicles
(University of Waterloo, 2022-05-12)Autonomous vehicles and quantum computers are two emerging technologies that will transform our world in the not-too-distant future. This thesis examines the safety and security of autonomous vehicles in a world where ... -
Structure in Stable Matching Problems
(University of Waterloo, 2016-12-14)In this thesis we provide two contributions to the study of structure in stable matching problems. The first contribution is a short new proof for the integrality of Rothblum’s linear description of the convex hull of ... -
A Study of Time Representation in a Class of Short Term Scheduling Problems
(University of Waterloo, 2016-08-17)The problem of scheduling operations has received significant attention from academia and industrial practitioners in the past few decades. A key decision in various scheduling operations problems is when to perform an ... -
Subdividing the cd-index
(University of Waterloo, 2016-04-28)This thesis aims to give the reader an introduction and overview of the cd-index of a poset, as well as establish some new results. We give a combinatorial proof of Ehrenborg and Karu's cd-index subdivision decomposition ... -
SUBMODULAR FUNCTIONS, GRAPHS AND INTEGER POLYHEDRA
(University of Waterloo, 2016-09-12)This thesis is a study of the faces of certain combinatorially defined polyhedra. In particular, we examine the vertices and facets of these polyhedra. Chapter 2 contains the essential mathematical background in polyhedral ... -
Sum-of-norms clustering: theoretical guarantee and post-processing
(University of Waterloo, 2020-09-11)Sum-of-norms clustering is a method for assigning n points in d-dimensional real space to K clusters, using convex optimization. Recently, Panahi et al. proved that sum-of-norms clustering is guaranteed to recover a mixture ... -
A Survey of Attacks on Multivariate Cryptosystems
(University of Waterloo, 2005)This thesis provides a survey of the attacks on multivariate cryptosystems. We begin by providing an outline of the general multivariate cryptosystem. Proceeding from there, we show that even with this level of detail, ... -
A survey of the trust region subproblem within a semidefinite framework
(University of Waterloo, 2000)Trust region subproblems arise within a class of unconstrained methods called trust region methods. The subproblems consist of minimizing a quadratic function subject to a norm constraint. This thesis is a survey of ... -
A survey on Traitor Tracing Schemes
(University of Waterloo, 2000)When intellectual properties are distributed over a broadcast network, the content is usually encrypted in a way such that only authorized users who have a certain set of keys, can decrypt the content. Some authorized ... -
Symmetries
(University of Waterloo, 2016-10-03)Automorphisms of graphs, hypergraphs and disgraphs are investigated. The invariance of the chromatic polynomial in the rotor effect is disproved. New invariance results are obtained. It is shown that given any integer k ... -
Techniques for Proving Approximation Ratios in Scheduling
(University of Waterloo, 2010-09-30)The problem of finding a schedule with the lowest makespan in the class of all flowtime-optimal schedules for parallel identical machines is an NP-hard problem. Several approximation algorithms have been suggested for ... -
Techniques of Side Channel Cryptanalysis
(University of Waterloo, 2001)The traditional model of cryptography examines the security of cryptographic primitives as mathematical functions. This approach does not account for the physical side effects of using these primitives in the real world. ... -
Technology Diffusion on Spiders
(University of Waterloo, 2017-08-29)There has been significant research about cascade effects that occur when information is spread through a network. Most models of such cascade effects are highly-localised, which means that they assume a node’s behaviour ... -
Theory of measurement-based quantum computing
(University of Waterloo, 2008-12-10)In the study of quantum computation, data is represented in terms of linear operators which form a generalized model of probability, and computations are most commonly described as products of unitary transformations, which ... -
Thin Trees in Some Families of Graphs
(University of Waterloo, 2018-04-25)Let 𝐺=(𝑉,𝐸) be a graph and let 𝑇 be a spanning tree of 𝐺. The thinness parameter of 𝑇 denoted by 𝜌(𝑇) is the maximum over all cuts of the proportion of the edges of 𝑇 in the cut. Thin trees play an important role ...