Browsing Theses by Subject "Combinatorics and Optimization"
Now showing items 1-20 of 141
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2-crossing critical graphs with a V8 minor
(University of Waterloo, 2012-01-17)The crossing number of a graph is the minimum number of pairwise crossings of edges among all planar drawings of the graph. A graph G is k-crossing critical if it has crossing number k and any proper subgraph of G has a ... -
Algebraic Aspects of Multi-Particle Quantum Walks
(University of Waterloo, 2012-12-04)A continuous time quantum walk consists of a particle moving among the vertices of a graph G. Its movement is governed by the structure of the graph. More formally, the adjacency matrix A is the Hamiltonian that determines ... -
Algebraic Methods and Monotone Hurwitz Numbers
(University of Waterloo, 2012-09-21)We develop algebraic methods to solve join-cut equations, which are partial differential equations that arise in the study of permutation factorizations. Using these techniques, we give a detailed study of the recently ... -
Algebraic Methods for Reducibility in Nowhere-Zero Flows
(University of Waterloo, 2007-09-25)We study reducibility for nowhere-zero flows. A reducibility proof typically consists of showing that some induced subgraphs cannot appear in a minimum counter-example to some conjecture. We derive algebraic proofs of ... -
Analyzing Quantum Cryptographic Protocols Using Optimization Techniques
(University of Waterloo, 2012-05-22)This thesis concerns the analysis of the unconditional security of quantum cryptographic protocols using convex optimization techniques. It is divided into the study of coin-flipping and oblivious transfer. We first examine ... -
Applications of Semidefinite Programming in Quantum Cryptography
(University of Waterloo, 2007-05-18)Coin-flipping is the cryptographic task of generating a random coin-flip between two mistrustful parties. Kitaev discovered that the security of quantum coin-flipping protocols can be analyzed using semidefinite programming. ... -
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 ... -
Approximation Algorithms for Path TSP, ATSP, and TAP via Relaxations
(University of Waterloo, 2015-07-29)Linear programming (LP) relaxations provide a powerful technique to design approximation algorithms for combinatorial optimization problems. In the first part of the thesis, we study the metric s-t path Traveling Salesman ... -
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 ... -
Bipartite Distance-Regular Graphs of Diameter Four
(University of Waterloo, 2014-08-11)Using a method by Godsil and Roy, bipartite distance-regular graphs of diameter four can be used to construct $\{0,\alpha\}$-sets, a generalization of the widely applied equiangular sets and mutually unbiased bases. In ... -
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 ... -
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 ... -
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 ... -
Classical Authenticated Key Exchange and Quantum Cryptography
(University of Waterloo, 2009-03-16)Cryptography plays an integral role in secure communication and is usually the strongest link in the chain of security. Yet security problems abound in electronic communication: spyware, phishing, denial of service, and ... -
Collision Finding with Many Classical or Quantum Processors
(University of Waterloo, 2011-08-31)In this thesis, we investigate the cost of finding collisions in a black-box function, a problem that is of fundamental importance in cryptanalysis. Inspired by the excellent performance of the heuristic rho method of ... -
Combinatorial Algorithms for Submodular Function Minimization and Related Problems
(University of Waterloo, 2015-05-19)Submodular functions are common in combinatorics; examples include the cut capacity function of a graph and the rank function of a matroid. The submodular function minimization problem generalizes the classical minimum cut ...