Browsing Combinatorics and Optimization by Title
Now showing items 278-297 of 436
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On Pairing-Based Signature and Aggregate Signature Schemes
(University of Waterloo, 2009-01-21)In 2001, Boneh, Lynn, and Shacham presented a pairing-based signature scheme known as the BLS signature scheme. In 2003, Boneh, Gentry, Lynn, and Shacham presented the first aggregate signature scheme called the BGLS ... -
On Polynomial-time Path-following Interior-point Methods with Local Superlinear Convergence
(University of Waterloo, 2016-09-30)Interior-point methods provide one of the most popular ways of solving convex optimization problems. Two advantages of modern interior-point methods over other approaches are: (1) robust global convergence, and (2) the ... -
On primal-dual interior-point algorithms for convex optimisation
(2015-09-29)This thesis studies the theory and implementation of interior-point methods for convex optimisation. A number of important problems from mathematics and engineering can be cast naturally as convex optimisation ... -
On primal-dual interior-point algorithms for convex optimisation
(2015-09-25)This thesis studies the theory and implementation of interior-point methods for convex optimisation. A number of important problems from mathematics and engineering can be cast naturally as convex optimisation ... -
On Prime-Order Elliptic Curves with Embedding Degrees 3, 4 and 6
(University of Waterloo, 2007-01-22)Bilinear pairings on elliptic curves have many cryptographic applications such as identity based encryption, one-round three-party key agreement protocols, and short signature schemes. The elliptic curves which are ... -
On Schnyder's Theorm
(University of Waterloo, 2010-08-20)The central topic of this thesis is Schnyder's Theorem. Schnyder's Theorem provides a characterization of planar graphs in terms of their poset dimension, as follows: a graph G is planar if and only if the dimension of ... -
On symmetric intersecting families of vectors
(Cambridge University Press, 2021-11)A family of vectors in [k]n is said to be intersecting if any two of its elements agree on at least one coordinate. We prove, for fixed k ≥ 3, that the size of any intersecting subfamily of [k]n invariant under a transitive ... -
On The Circuit Diameters of Some Combinatorial Polytopes
(University of Waterloo, 2017-09-20)The combinatorial diameter of a polytope P is the maximum value of a shortest path between two vertices of P, where the path uses the edges of P only. In contrast to the combinatorial diameter, the circuit diameter of P ... -
On the Crossing Numbers of Complete Graphs
(University of Waterloo, 2006)In this thesis we prove two main results. The Triangle Conjecture asserts that the convex hull of any optimal rectilinear drawing of <em>K<sub>n</sub></em> must be a triangle (for <em>n</em> ≥ 3). We prove that, ... -
On The Density of Binary Matroids Without a Given Minor
(University of Waterloo, 2016-12-21)This thesis is motivated by the following question: how many elements can a simple binary matroid with no $\PG(t,2)$-minor have? This is a natural analogue of questions asked about the density of graphs in minor-closed ... -
On the effectiveness of isogeny walks for extending cover attacks on elliptic curves
(University of Waterloo, 2016-08-23)Cryptographic systems based on the elliptic curve discrete logarithm problem (ECDLP) are widely deployed in the world today. In order for such a system to guarantee a particular security level, the elliptic curve selected ... -
On the Efficiency and Security of Cryptographic Pairings
(University of Waterloo, 2012-12-19)Pairing-based cryptography has been employed to obtain several advantageous cryptographic protocols. In particular, there exist several identity-based variants of common cryptographic schemes. The computation of a single ... -
On the Evolutionary Design of Quantum Circuits
(University of Waterloo, 2005)The goal of this work is to understand the application of the evolutionary programming approach to the problem of quantum circuit design. This problem is motivated by the following observations: <ul> <li>In order to ... -
On the Excluded Minors for Dyadic Matroids
(University of Waterloo, 2019-01-17)The study of the class of dyadic matroids, the matroids representable over both $GF(3)$ and $GF(5)$, is a natural step to finding the excluded minors for $GF(5)$-representability. In this thesis we characterize the ternary ... -
On the Integrality Gap of Directed Steiner Tree Problem
(University of Waterloo, 2014-05-27)In the Directed Steiner Tree problem, we are given a directed graph G = (V,E) with edge costs, a root vertex r ∈ V, and a terminal set X ⊆ V . The goal is to find the cheapest subset of edges that contains an r-t path for ... -
On the orientation of hypergraphs
(University of Waterloo, 2011-01-13)This is an expository thesis. In this thesis we study out-orientations of hypergraphs, where every hyperarc has one tail vertex. We study hypergraphs that admit out-orientations covering supermodular-type connectivity ... -
On the Polyhedral Lift-and-Project Rank Conjecture for the Fractional Stable Set Polytope
(University of Waterloo, 2008-01-16)In this thesis, we study the behaviour of Lovasz and Schrijver's lift-and-project operators N and N_0 while being applied recursively to the fractional stable set polytope of a graph. We focus on two related conjectures ... -
On the Power and Limitations of Shallow Quantum Circuits
(University of Waterloo, 2022-09-01)Constant-depth quantum circuits, or shallow quantum circuits, have been shown to exhibit behavior that is uniquely quantum. This thesis explores the power and limitations of constant-depth quantum circuits, in particular ... -
On the Relationship between Conjugate Gradient and Optimal First-Order Methods for Convex Optimization
(University of Waterloo, 2014-01-23)In a series of work initiated by Nemirovsky and Yudin, and later extended by Nesterov, first-order algorithms for unconstrained minimization with optimal theoretical complexity bound have been proposed. On the other hand, ... -
On the Role of Partition Inequalities in Classical Algorithms for Steiner Problems in Graphs
(University of Waterloo, 2006)The Steiner tree problem is a classical, well-studied, $\mathcal{NP}$-hard optimization problem. Here we are given an undirected graph $G=(V,E)$, a subset $R$ of $V$ of terminals, and non-negative costs $c_e$ for all ...