Combinatorics and Optimization
This is the collection for the University of Waterloo's Department of Combinatorics and Optimization .
Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).
Waterloo faculty, students, and staff can contact us or visit the UWSpace guide to learn more about depositing their research.
Recent deposits

A computational study of practical issues arising in shortterm scheduling of a multipurpose facility
(University of Waterloo, 20190123)This thesis focuses on two important considerations when solving short term scheduling problems for multipurpose facilities: deciding when rescheduling should be performed and choosing efficient time representations for ... 
On the Excluded Minors for Dyadic Matroids
(University of Waterloo, 20190117)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 ... 
Split Cuts From Sparse Disjunctions
(University of Waterloo, 20190116)Cutting planes are one of the major techniques used in solving MixedInteger Linear Programming (MIP) models. Various types of cuts have long been exploited by MIP solvers, leading to stateoftheart performance in practice. ... 
Edge State Transfer
(University of Waterloo, 20190111)Let G be a graph and let t be a positive real number. Then the evolution of the continuous quantum walk defined on G is described by the transition matrix U(t)=exp(itH).The matrix H is called Hamiltonian. So far the most ... 
Quantum Walks on Oriented Graphs
(University of Waterloo, 20190111)This thesis extends results about periodicity and perfect state transfer to oriented graphs. We prove that if a vertex a is periodic, then elements of the eigenvalue support lie in Z √∆ for some squarefree negative ... 
Sensitivity Analysis and Robust Optimization: A Geometric Approach for the Special Case of Linear Optimization
(University of Waterloo, 20181221)In this thesis, we study the special case of linear optimization to show what may affect the sensitivity of the optimal value function under data uncertainty. In this special case, we show that the robust optimization ... 
The Erdős Pentagon Problem
(University of Waterloo, 20181220)The Erdős pentagon problem asks about the maximum number of copies of C_5 that one can find in a trianglefree graph. This problem was posed in 1984, but was not resolved until 2012. In this thesis, we aim to capture the ... 
Matchings and Representation Theory
(University of Waterloo, 20181220)In this thesis we investigate the algebraic properties of matchings via representation theory. We identify three scenarios in different areas of combinatorial mathematics where the algebraic structure of matchings gives ... 
An integrated personnel allocation and machine scheduling problem for industrial size multipurpose plants
(Elsevier, 20180101)This paper describes the development and implementation of an optimization model to solve the integrated problem of personnel allocation and machine scheduling for industrial size multipurpose plants. Although each of these ... 
On Eulerian orientations of evendegree hypercubes
(Elsevier, 20180901)It is well known that every Eulerian orientation of an Eulerian 2kedge connected (undirected) graph is strongly kedge connected. A longstanding goal in the area is to obtain analogous results for other types of connectivity, ... 
Discrete Quantum Walks on Graphs and Digraphs
(University of Waterloo, 20180926)This thesis studies various models of discrete quantum walks on graphs and digraphs via a spectral approach. A discrete quantum walk on a digraph $X$ is determined by a unitary matrix $U$, which acts on complex functions ... 
Results on Chromatic Polynomials Inspired by a Correlation Inequality of G.E. Farr
(University of Waterloo, 20180925)In1993 Graham Farr gave a proof of a correlation inequality involving colourings of graphs. His work eventually led to a conjecture that number of colourings of a graph with certain properties gave a logconcave sequence. ... 
Ordinary and Generalized Circulation Algebras for Regular Matroids
(University of Waterloo, 20180919)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 ... 
NonConstructivity in Security Proofs
(University of Waterloo, 20180910)In the field of cryptography, one generally obtains assurances for the security of a cryptographic protocol by giving a reductionist security proof, which is comprised of a reduction from breaking a mathematical problem ... 
Acyclic Colouring of Graphs on Surfaces
(University of Waterloo, 20180904)An acyclic kcolouring of a graph G is a proper kcolouring of G with no bichromatic cycles. In 1979, Borodin proved that planar graphs are acyclically 5colourable, an analog of the Four Colour Theorem. Kawarabayashi and ... 
Density and Structure of HomomorphismCritical Graphs
(University of Waterloo, 20180822)Let $H$ be a graph. A graph $G$ is $H$critical if every proper subgraph of $G$ admits a homomorphism to $H$, but $G$ itself does not. In 1981, Jaeger made the following conjecture concerning oddcycle critical graphs: ... 
Induction Relations in the Symmetric Groups and JucysMurphy Elements
(University of Waterloo, 20180816)Transitive factorizations faithfully encode many interesting objects. The wellknown ones include ramified coverings of the sphere and hypermaps. Enumeration of specific classes of such objects have been known for quite ... 
Spectral properties of tensor products of channels
(Elsevier, 20180915)We investigate spectral properties of the tensor products of two completely positive and trace preserving linear maps (also known as quantum channels) acting on matrix algebras. This leads to an important question of when ... 
Action of degenerate Bethe operators on representations of the symmetric group
(University of Waterloo, 20180524)Degenerate Bethe operators are elements defined by explicit sums in the center of the group algebra of the symmetric group. They are useful on account of their relation to the GelfandZetlin algebra and the YoungJucysMurphy ... 
The Capacitated Matroid Median Problem
(University of Waterloo, 20180518)In this thesis, we study the capacitated generalization of the Matroid Median Problem which is a generalization of the classical clustering problem called the kMedian problem. In the capacitated matroid median problem, ...