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.
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Induced Binary Submatroids
(University of Waterloo, 2021-07-21)The notion of induced subgraphs is extensively studied in graph theory. An example is the famous Gy\'{a}rf\'{a}s-Sumner conjecture, which asserts that given a tree $T$ and a clique $K$, there exists a constant $c$ such ... -
Fractional refinements of integral theorems
(University of Waterloo, 2021-07-09)The focus of this thesis is to take theorems which deal with ``integral" objects in graph theory and consider fractional refinements of them to gain additional structure. A classic theorem of Hakimi says that for an ... -
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 ... -
Computing the Nucleolus of Matching and b-Matching Games
(University of Waterloo, 2021-05-21)In the classical weighted matching problem the optimizer is given a graph with edge weights and their goal is to find a matching which maximizes the sum of the weights of edges in the matching. It is typically assumed in ... -
Simple Termination Criteria for Stochastic Gradient Descent Algorithm
(University of Waterloo, 2021-04-09)Stochastic gradient descent (SGD) algorithm is widely used in modern mathematical optimization. Because of its scalability and ease of implementation, SGD is usually preferred to other methods including the gradient descent ... -
Tolls For Atomic Congestion Games
(University of Waterloo, 2021-02-26)In games where selfish players compete for resources, they often arrive at equilibria that are less desirable than the social optimum. To combat this inefficiency, it is common for some central authority to place tolls on ... -
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 ... -
Relaxations of the Maximum Flow Minimum Cut Property for Ideal Clutters
(University of Waterloo, 2021-01-29)Given a family of sets, a covering problem consists of finding a minimum cost collection of elements that hits every set. This objective can always be bound by the maximum number of disjoint sets in the family, we refer ... -
Comparing Classical Portfolio Optimization and Robust Portfolio Optimization on Black Swan Events
(University of Waterloo, 2021-01-29)Black swan events, such as natural catastrophes and manmade market crashes, historically have a drastic negative influence on investments; and there is a discrepancy on losses caused by these two types of disasters. In ... -
Craniosynostosis Surgery: A Study of Rearrangement
(University of Waterloo, 2020-12-22)Cranial vault remodeling, a form of skull surgery is currently performed according to intuition developed over years of experience. The problem of how to best perform this surgery has not yet thoroughly been studied by ... -
Quantum Compression and Quantum Learning via Information Theory
(University of Waterloo, 2020-12-21)This thesis consists of two parts: quantum compression and quantum learning theory. A common theme between these problems is that we study them through the lens of information theory. We first study the task of visible ... -
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 ... -
The complexity of some set-partitioning formulations for the vehicle routing problem with stochastic demands
(University of Waterloo, 2020-10-28)The capacitated vehicle routing problem with stochastic demands (CVRPSD) is a variant of the deterministic capacitated vehicle routing problem (CVRP). The CVRP consists of planning routes for vehicles with a given capacity ... -
On Combinatorics, Integrability and Puzzles
(University of Waterloo, 2020-10-23)In the last decade, many old and new results in combinatorics have been shown using the theory of quantum integrable systems from particle physics. The key to solving such problems is the derivation of an underlying ... -
Sum-of-norms clustering: theoretical guarantee and post-processing
(University of Waterloo, 2020-09-11)Sum-of-norms clustering is a method for assigning n points in d-dimensional real space to K clusters, using convex optimization. Recently, Panahi et al. proved that sum-of-norms clustering is guaranteed to recover a mixture ... -
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 ... -
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 ... -
Smoothening Functions and the Homomorphism Learning Problem
(University of Waterloo, 2020-09-02)This thesis is an exploration of certain algebraic and geometrical aspects of the Learning With Errors (LWE) problem introduced in Reg05. On the algebraic front, we view it as a Learning Homomorphisms with Noise problem, ... -
Sparsity in Critical Graphs with Small Clique Number
(University of Waterloo, 2020-08-27)In 1998, Reed conjectured that for every graph $G$, $\chi(G) \leq \lceil \frac{1}{2}(\Delta(G)+1+\omega(G)) \rceil$, and proved that there exists $\varepsilon > 0$ such that $\chi(G) \leq \lceil (1 - \varepsilon)(\Delta(G)+1) ... -
Noisy Interactive Quantum Communication
(University of Waterloo, 2020-08-25)We consider the problem of implementing two-party interactive quantum communication over noisy channels, a necessary endeavor if we wish to fully reap quantum advantages for communication. For an arbitrary protocol with n ...
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