Browsing Combinatorics and Optimization by Type "Master Thesis"
Now showing items 21-40 of 257
-
Approximate Private Quantum Channels
(University of Waterloo, 2006)This thesis includes a survey of the results known for private and approximate private quantum channels. We develop the best known upper bound for ε-randomizing maps, <em>n</em> + 2log(1/ε) + <em>c</em> ... -
Approximating Minimum-Size 2-Edge-Connected and 2-Vertex-Connected Spanning Subgraphs
(University of Waterloo, 2017-04-27)We study the unweighted 2-edge-connected and 2-vertex-connected spanning subgraph problems. A graph is 2-edge-connected if it is connected on removal of an edge, and it is 2-vertex-connected if it is connected on removal ... -
Approximation Algorithms for (S,T)-Connectivity Problems
(University of Waterloo, 2010-08-03)We study a directed network design problem called the $k$-$(S,T)$-connectivity problem; we design and analyze approximation algorithms and give hardness results. For each positive integer $k$, the minimum cost $k$-vertex ... -
Approximation Algorithms for Graph Protection Problems
(University of Waterloo, 2015-05-22)We study a budgeted cut problem known as Graph Protection, where the goal is to remove edges of a given graph in order to protect valuable nodes from stochastic, infectious threats. This problem was recently proposed ... -
Aspects of Quantum Field Theory in Enumerative Graph Theory
(University of Waterloo, 2022-10-24)While a quantum field theorist has many uses for mathematics of all kinds, the relationship between quantum field theory and mathematics is far too fluid in the world of modern research to be described as the simple provision ... -
Assessing the Trainability of the Variational Quantum State Diagonalization Algorithm at Scale
(University of Waterloo, 2022-04-28)Quantum algorithm development is a famously difficult problem. The lack of intuition concerning the quantum realm makes constructing quantum algorithms which solve partic- ular problems of interest difficult. In addition, ... -
Augmenting Trees to Achieve 2-Node-Connectivity
(University of Waterloo, 2020-09-02)This thesis focuses on the Node-Connectivity Tree Augmentation Problem (NC-TAP), formally defined as follows. The first input of the problem is a graph G which has vertex set V and edge set E. We require |V| >= 3 to avoid ... -
Batch Verification of Elliptic Curve Digital Signatures
(University of Waterloo, 2015-04-20)This thesis investigates the efficiency of batching the verification of elliptic curve signatures. The first signature scheme considered is a modification of ECDSA proposed by Antipa et al.\ along with a batch verification ... -
A Blueprint for Semidefinite Relaxations of Binary-Constrained Quadratic Programs Computing tight bounds on NP-hard problems using ADMM
(University of Waterloo, 2020-12-18)This thesis looks at the solution techniques of two NP-hard, large scale problems, the quadratic assignment problem, QAP, and the side chain positioning, SCP, problem. We summarize existing approaches from and look at the ... -
Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem
(University of Waterloo, 2009-01-22)The Boneh-Boyen signature scheme is a short signature scheme which is provably secure in the standard model under the q-Strong Diffie-Hellman (SDH) assumption. The primary objective of this thesis is to examine the ... -
Building Networks in the Face of Uncertainty
(University of Waterloo, 2011-08-26)The subject of this thesis is to study approximation algorithms for some network design problems in face of uncertainty. We consider two widely studied models of handling uncertainties - Robust Optimization and Stochastic ... -
The Capacitated Matroid Median Problem
(University of Waterloo, 2018-05-18)In this thesis, we study the capacitated generalization of the Matroid Median Problem which is a generalization of the classical clustering problem called the k-Median problem. In the capacitated matroid median problem, ... -
Capacitated Network Design on Outerplanar Graphs
(University of Waterloo, 2020-09-03)Network design problems model the efficient allocation of resources like routers, optical fibres, roads, canals etc. to effectively construct and operate critical infrastructures. In this thesis, we consider the capacitated ... -
A Characterization of LYM and Rank Logarithmically Concave Partially Ordered Sets and Its Applications
(University of Waterloo, 2010-01-21)The LYM property of a finite standard graded poset is one of the central notions in Sperner theory. It is known that the product of two finite standard graded posets satisfying the LYM properties may not have the LYM ... -
Characterization of non-universal two-qubit Hamiltonians
(University of Waterloo, 2009-12-16)It is known that almost all 2-qubit gates are universal for quantum computing (Lloyd 1995; Deutsch, Barenco, Eckert 1995). However, an explicit characterization of non-universal 2-qubit gates is not known. We consider a ... -
Chosen Ciphertext Security from Zero Knowledge Proofs
(University of Waterloo, 2023-08-24)When designing encryption schemes, there are different levels of security that one can achieve. Of the two main security levels, cryptographers generally strive for the stronger notion of chosen ciphertext attack (CCA) ... -
Circle Graph Obstructions
(University of Waterloo, 2017-08-31)In this thesis we present a self-contained proof of Bouchet’s characterization of the class of circle graphs. The proof uses signed graphs and is analogous to Gerards’ graphic proof of Tutte’s excluded-minor characterization ... -
Classical and Quantum Algorithms for Isogeny-based Cryptography
(University of Waterloo, 2015-09-30)Isogeny-based cryptography using supersingular elliptic curves --- most prominently, the constructions of De Feo-Jao-Plut --- is one of the few practical candidates for post-quantum public key cryptography. Its formidable ... -
Clifford Simulation: Techniques and Applications
(University of Waterloo, 2021-05-28)Despite the widespread belief that quantum computers cannot be efficiently simulated classically, efficient simulation is known to be possible in certain restricted regimes. In particular, the Gottesman-Knill theorem states ... -
Clique minors in dense matroids
(University of Waterloo, 2022-09-23)The objective of this thesis is to bound the number of points a $U_{2,\ell+2}$- and $M(K_{k+1})$-minor-free matroid has. We first prove that a sufficiently large matroid will contain a structure called a tower. We then use ...