Browsing Combinatorics and Optimization by Title
Now showing items 298-317 of 436
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On the Security of Leakage Resilient Public Key Cryptography
(University of Waterloo, 2012-04-30)Side channel attacks, where an attacker learns some physical information about the state of a device, are one of the ways in which cryptographic schemes are broken in practice. "Provably secure" schemes are subject to these ... -
On the Strongly Connected Components of Random Directed Graphs with Given Degree Sequences
(University of Waterloo, 2016-08-24)A strongly connected component of a directed graph G is a maximal subgraph H of G such that for each pair of vertices u and v in H, there is a directed path from u to v and a directed path from v to u in H. A strongly ... -
On Vegh's Strongly Polynomial Algorithm for Generalized Flows
(University of Waterloo, 2014-05-22)This thesis contains an exposition of the new strongly polynomial algorithm for the generalized flow problem by Laszlo Vegh (2013). It has been a long-standing open question whether such an algorithm exists, until it was ... -
Open Shortest Path First Routing Under Random Early Detection
(Wiley, 2018-03-01)In this article, we consider a variant of Open Shortest Path First (OSPF) routing that accounts for Random Early Detection (RED), an Active Queue Management method for backbone networks. In the version of OSPF we consider ... -
Optimal Pairings on BN Curves
(University of Waterloo, 2011-08-26)Bilinear pairings are being used in ingenious ways to solve various protocol problems. Much research has been done on improving the efficiency of pairing computations. This thesis gives an introduction to the Tate pairing ... -
An Optimization Problem of Internet Routing
(University of Waterloo, 2014-09-23)As the Internet usage grows, existing network infrastructure must deal with increasing demand. One way to deal with this is to increase network capacity, and another, is to set network parameters appropriately. In this ... -
An Optimizing Pulse Sequence Compiler for NMR QIP
(University of Waterloo, 2003)Quantum information processing is a multi-disciplinary science involving physics, mathematics, computer science, and even quantum chemistry. It is centred around the idea of manipulating physical systems at the quantum ... -
Ordinary and Generalized Circulation Algebras for Regular Matroids
(University of Waterloo, 2018-09-19)Let E be a finite set, and let R(E) denote the algebra of polynomials in indeterminates (x_e)_{e in E}, modulo the squares of these indeterminates. Subalgebras of R(E) generated by homogeneous elements of degree 1 have ... -
Packing and Covering Odd (u,v)-trails in a Graph
(University of Waterloo, 2016-09-27)In this thesis, we investigate the problem of packing and covering odd $(u,v)$-trails in a graph. A $(u,v)$-trail is a $(u,v)$-walk that is allowed to have repeated vertices but no repeated edges. We call a trail \emph{odd} ... -
Packing Directed Joins
(University of Waterloo, 2004)Edmonds and Giles conjectured that the maximum number of directed joins in a packing is equal to the minimum weight of a directed cut, for any weighted directed graph. This is a generalization of Woodall's Conjecture ... -
Parking Functions and Related Combinatorial Structures.
(University of Waterloo, 2001)The central topic of this thesis is parking functions. We give a survey of some of the current literature concerning parking functions and focus on their interaction with other combinatorial objects; namely noncrossing ... -
Partition Algebras and Kronecker Coefficients
(University of Waterloo, 2015-08-28)Classical Schur-Weyl duality relates the representation theory of the general linear group to the representation theory of the symmetric group via their commuting actions on tensor space. With the goal of studying Kronecker ... -
Partitioning Pauli Operators: in Theory and in Practice
(University of Waterloo, 2019-09-04)Measuring the expectation value of Pauli operators on prepared quantum states is a fundamental task in the variational quantum eigensolver. Simultaneously measuring sets of operators allows for fewer measurements and an ... -
Path Tableaux and the Combinatorics of the Immanant Function
(University of Waterloo, 2013-04-29)Immanants are a generalization of the well-studied determinant and permanent. Although the combinatorial interpretations for the determinant and permanent have been studied in excess, there remain few combinatorial ... -
Perfect Hash Families: Constructions and Applications
(University of Waterloo, 2003)Let <b>A</b> and <b>B</b> be finite sets with |<b>A</b>|=<i>n</i> and |<b>B</b>|=<i>m</i>. An (<i>n</i>,<i>m</i>,<i>w</i>)-<i>perfect hash</i> family</i> is a collection <i>F</i> of functions from <b>A</b> to <b>B</b> ... -
Piercing axis-parallel boxes
(The Electronic Journal of Combinatorics, 2018)Let F be a finite family of axis-parallel boxes in Rd such that F contains no k + 1 pairwise disjoint boxes. We prove that if F contains a subfamily M of k pairwise disjoint boxes with the property that for every F E F ... -
Planar graphs without 3-cycles and with 4-cycles far apart are 3-choosable
(University of Waterloo, 2016-09-16)A graph G is said to be L-colourable if for a given list assignment L = {L(v)|v ∈ V (G)} there is a proper colouring c of G such that c(v) ∈ L(v) for all v in V (G). If G is L-colourable for all L with |L(v)| ≥ k for all ... -
Plethysms of Chromatic and Tutte Symmetric Functions
(The Electronic Journal of Combinatorics, 2022)Plethysm is a fundamental operation in symmetric function theory, derived directly from its connection with representation theory. However, it does not admit a simple combinatorial interpretation, and finding coefficients ... -
Polyhedral Diameters and Applications to Optimization
(University of Waterloo, 2022-09-01)The Simplex method is the most popular algorithm for solving linear programs (LPs). Geometrically, it moves from an initial vertex solution to an improving neighboring one, selected according to a pivot rule. Despite decades ... -
Polynomial bounds for chromatic number II: Excluding a star-forest
(Wiley, 2022-10)The Gyárfás–Sumner conjecture says that for every forest H, there is a function fH such that if G is H-free then x(G) ≤ fH(w(G)) (where x,w are the chromatic number and the clique number of G). Louis Esperet conjectured ...