Theory and Algorithms Commons^™

Breadquest: Enhancing Roguelike Accessibility Through Procedural Generation And Thematic Design, Hahns Pena

Computer Science and Software Engineering

BreadQuest is a top-down roguelike dungeon crawler with a whimsical dessert theme that aims to make the genre more accessible while preserving strategic depth and replayability. Players explore procedurally generated dungeons, fight pastry-themed enemies, and collect bakery-inspired items that support a flavor-elemental combat system, with each run offering unique layouts, encounters, and rewards. Built in Unity with a modular, data-driven architecture, the game uses procedural generation techniques like Binary Space Partitioning, Voronoi diagrams, and Perlin noise to create varied and replayable levels. The project emphasizes approachable gameplay, cultural dessert inspiration, and replayability, with success evaluated through playtesting and player feedback.

Crab: A Novel Clustering Score Using Clustering With Rivals And Buddies For Unsupervised Learning, Allen Choi

Master's Theses

Unsupervised clustering algorithms today are used across a wide variety of fields such as biology, engineering, and industry in order to classify observations into groups where labels are not provided. This can provide important latent information regarding the observations within groups, as well as insight regarding the groups themselves. In order to judge the optimal number of clusters for an unsupervised clustering algorithm, many methods exist such as the Elbow Method and Silhouette Score; however, these methods come with drawbacks and are not necessarily flexible across many unsupervised methods. We present a novel clustering score framework relying on a resampling-based …

Empirical Comparsion Of Traveling Salesperson Approximation Algorithms, Shayan Daijavad

Master's Theses

The traveling salesperson problem deals with optimizing the route a traveling sales- person might take to visit a set of places exactly once and return back to their starting point. The problem is NP-hard, and it is hard to approximate in general, but special cases have many approximation algorithms, which come with tradeoffs. In this thesis we compare the runtime, approximation ratio, and overall implementation complexity of two approximation algorithms for the Euclidean version of the problem, a classical 2-approximation algorithm and the multifragment heuristic. We run both algorithms on randomly generated point sets and real world data from TSPLIB. …

An Evaluation Of Road Network Structure As A Predictor Of Traffic Volume, Colin M. Mcdonald

Master's Theses

This thesis evaluates the relationships between various graph theory metrics and taxi traffic volume for the cities of San Francisco, California and Porto, Portugal. We also evaluate a modified betweenness centrality metric which incorporates the count of distinct origin-destination pairs from the taxi data as the weight function. This thesis extends a paper by Pengyao Ye, Bo Wu, and Wenbo Fan by reducing circularity through a temporal train-test split and by comparing both line-graph and primal-graph formulations of betweenness centrality.

We found that past traffic volume is almost perfectly correlated with future traffic volume and that the modified betweenness centrality …

Demystifying Hardware Formal Verification For Undergraduate Education: A Risc-V Processor Case Study With Coursework Implementation, Riley A. Peters

Master's Theses

Hardware verification engineers apply formal methods to prove that a digital device always behaves according to its specification. This differs from traditional functional verification, in which engineers establish correctness by repeatedly sending test inputs to the device and comparing the outputs against a reference model. With the growing complexity of integrated circuits, the demand for digital verification engineers with formal methods experience has continued to increase. However, California Polytechnic State University: San Luis Obispo's current curriculum lacks dedicated material to prepare students for these roles.

This thesis seeks to address the lack of formal methods material through two efforts. First, …

A Scalable Iteration Of The Horizon Simulation Framework Using Multithreading Techniques, Jason E. Beals

Master's Theses

The Horizon Simulation Framework (HSF) occupies a unique space in the modern aerospace modeling landscape, enabling flexible, modular modeling of mission-level agent behavior through an object-oriented, hierarchical design. HSF's hallmark breadth-first search scheduling algorithm explores a "multiverse" of possible mission execution pathways, enabling exhaustive evaluation of schedule combinations against user-defined heuristics.

As aerospace systems become increasingly complex, HSF faces critical challenges in establishing verifiable, deterministic behavior. The framework's core scheduling algorithm had not undergone systematic validation, leaving questions about temporal consistency, state management correctness, and reproducibility across different program executions. Furthermore, the exponential growth of schedule combinations creates computational bottlenecks …

Filling Gaps In Scientific Data Sets Using Physics Informed Neural Networks: A Case Study In Velocity Fields, Ellen Saunders

Master's Theses

Gaps in scientific data sets are a persistent issue for researchers in a variety of fields, and while nothing makes up for missing out on real data, well-simulated synthetic data can be a useful tool. In the world of image processing, machine learning techniques have become quite sophisticated at taking an image with a missing component and filling in that space with something believable. The aim of this thesis is to take machine learning techniques similar to what gets used in image processing and repurpose them to infill gaps in scientific data sets in a realistic manner. This thesis compares …

Topodino: Self-Supervised Topological Representation Learning For Neuronal Morphologies, Yasser Binbisher

Master's Theses

Neuronal cell types are categorized by transcriptomic identity, yet their morphological heterogeneity defies this classification. In response, researchers have adopted unsupervised graph representation learning as a tool to reveal morphological variation within single-class transcriptomic types. However, the complex geometry of neuronal morphology—especially long axons and dense dendrites—challenges graph neural networks, which struggle with message propagation across extended structures. To mitigate this, current approaches enforce sub-sampling on neuronal graphs and omit axons entirely, sacrificing critical biological features for computational efficiency. To overcome this trade-off, this thesis introduces TopoDINO, a self-supervised, topology-aware representation learning model designed to preserve the full hierarchical organization …

Counting Catalan: An Experimental Evaluation Of The Mixing Time For The Triangulation Markov Chain, Roy Gotlieb

Master's Theses

Monte Carlo Markov chains (MCMCs) are used in many areas as a way to model a system’s behavior. By running a probabilistic simulation on a system’s state space, we can estimate properties of the system that could be untenable to directly compute. It is of interest to determine how quickly a Markov chain mixes\textemdash that is, settles into its stationary distribution. One such chain is induced by taking a binary search tree and performing a rotation or flip on one of its edges. We know that this chain eventually settles into the uniform distribution, but the time complexity bounds on …

Investigation Of Social Networks Upon Academic Performance And Mental Health, Rachel Izenson

Master's Theses

It has been shown that computing students have a statistically significantly lower overall sense of belongingness compared to other science students. A sense of community is important for many reasons. For example, there are studies that show that a student's sense of belonging correlates with improved academic performance. Our research aims to analyze the sense of belonging among computing students at Cal Poly San Luis Obispo through a network science lens. We surveyed for their sense of belonging, as well as their social network, to understand how friendships impact one's sense of belonging. When student responses were split by gender, …

Optimizing Sensor Placements For Fixed Source Localization: A Distinct Subset Distance Sum Problem, Peter Chinh

College of Engineering Summer Undergraduate Research Program

This research addresses the problem of optimizing sensor placements for fixed source localization using distinct subset distance sums. Given a line L in R² and a set P of n points on one side of L, we seek to locate a minimal set S of points on L such that for any two distinct subsets Q and R of P, there exists a point s∈S where the sum of reciprocal distances from Q to s uniquely identifies Q. Our results show that a minimal sensor set S of size 1 is always feasible, but computing this set exactly proves …

Empirical Support For Algorithmic Conjectures, Shayan Daijavad

College of Engineering Summer Undergraduate Research Program

Our project focuses on a particular Markov Chain Monte Carlo algorithm, with applications in statistical physics, known as hardcore model Glauber dynamics. The target distribution of Glauber dynamics is a distribution of all of the independent sets within a graph. An independent set is a set of vertices within a graph with no two vertices in the set containing an edge between them. Our goal is to find whether or not the Glauber dynamics for sampling independent sets on trees mixes in time O(nlogn), and determining how the mixing time changes if we bias the algorithm in favor of larger …

Leveraging Tradespace-Exploration For A Senior Project Team Formation Application, Miguel Saenz

College of Engineering Summer Undergraduate Research Program

This project revolves around the development of an app in MATLAB that leverages the VASSAR rule-based system and a genetic algorithm to form groups of teams for the Mechanical Engineering Senior Design project class. We leveraged the iterative design process to eventually attain a functional app with a reasonable runtime that works provided correctly formatted rulesheets describing student project preference and member preference.

Pain Points: Cluster Analysis In Chronic Pain Networks, Iris W. Ho

Master's Theses

Chronic pain is a pervasive health issue, affecting a significant portion of the population and posing complex challenges due to its diverse etiology and individualized impact. To address this complexity, there is a growing interest in grouping chronic pain patients based on their unique treatment needs. While various methodologies for patient grouping have emerged, leveraging graph-based approaches to produce and evaluate such groupings remains largely unexplored. Recent studies have shown promise in integrating knowledge graphs into exploring patient similarity across different biological domains, indicating potential avenues for research. Additionally, there is a growing interest in investigating patient similarity networks, highlighting …

Electronic Note-String Detector, Gavin Garcia-Rossi, Tommy Smail

Electrical Engineering

As the virtual space has become a dominant part of everyone’s day-to-day lives, many normal face-to-face interactions and services have not yet been facilitated by adapting technology. One of these prevailing areas is music lessons. Over Zoom meetings, or other virtual platforms, it is tremendously challenging to teach students. These challenges include recognizing student mistakes audibly and visually, and being able to give confident feedback on the incorrect notes played by learning musicians. Without having to delve into improving the complex systems that would be required to improve audio, video, and connection quality of these connections, we have another solution …

Foundations Of Memory Capacity In Models Of Neural Cognition, Chandradeep Chowdhury

Master's Theses

A central problem in neuroscience is to understand how memories are formed as a result of the activities of neurons. Valiant’s neuroidal model attempted to address this question by modeling the brain as a random graph and memories as subgraphs within that graph. However the question of memory capacity within that model has not been explored: how many memories can the brain hold? Valiant introduced the concept of interference between memories as the defining factor for capacity; excessive interference signals the model has reached capacity. Since then, exploration of capacity has been limited, but recent investigations have delved into the …

Neural Tabula Rasa: Foundations For Realistic Memories And Learning, Patrick R. Perrine

Master's Theses

Understanding how neural systems perform memorization and inductive learning tasks are of key interest in the field of computational neuroscience. Similarly, inductive learning tasks are the focus within the field of machine learning, which has seen rapid growth and innovation utilizing feedforward neural networks. However, there have also been concerns regarding the precipitous nature of such efforts, specifically in the area of deep learning. As a result, we revisit the foundation of the artificial neural network to better incorporate current knowledge of the brain from computational neuroscience. More specifically, a random graph was chosen to model a neural system. This …

Wasm-Pbchunk: Incrementally Developing A Racket-To-Wasm Compiler Using Partial Bytecode Compilation, Adam C. Perlin

Master's Theses

Racket is a modern, general-purpose programming language with a language-oriented focus. To date, Racket has found notable uses in research and education, among other applications. To expand the reach of the language, there has been a desire to develop an efficient platform for running Racket in a web-based environment. WebAssembly (Wasm) is a binary executable format for a stack-based virtual machine designed to provide a fast, efficient, and secure execution environment for code on the web. Wasm is primarily intended to be a compiler target for higher-level languages. Providing Wasm support for the Racket project may be a promising way …

A Novel Approach To Extending Music Using Latent Diffusion, Keon Roohparvar, Franz J. Kurfess

Master's Theses

Using deep learning to synthetically generate music is a research domain that has gained more attention from the public in the past few years. A subproblem of music generation is music extension, or the task of taking existing music and extending it. This work proposes the Continuer Pipeline, a novel technique that uses deep learning to take music and extend it in 5 second increments. It does this by treating the musical generation process as an image generation problem; we utilize latent diffusion models (LDMs) to generate spectrograms, which are image representations of music. The Continuer Pipeline is able to …

Solving Fjssp With A Genetic Algorithm, Michael John Srouji

Computer Science and Software Engineering

The Flexible Job Shop Scheduling Problem is an NP-Hard combinatorial problem. This paper aims to find a solution to this problem using genetic algorithms, and discuss the effectiveness of this. Initially, I did exploratory work on whether neural networks would be effective or not, and found a lot of trade offs between using neural networks and chromosome sequencing. In the end, I decided to use chromosome sequencing over neural networks, due to the scope of my problem being on a small scale rather than on a large scale.

Therefore, the genetic algorithm was implemented using chromosome sequencing. My chromosomes were …

Legislative Language For Success, Sanjana Gundala

Master's Theses

Legislative committee meetings are an integral part of the lawmaking process for local and state bills. The testimony presented during these meetings is a large factor in the outcome of the proposed bill. This research uses Natural Language Processing and Machine Learning techniques to analyze testimonies from California Legislative committee meetings from 2015-2016 in order to identify what aspects of a testimony makes it successful. A testimony is considered successful if the alignment of the testimony matches the bill outcome (alignment is "For" and the bill passes or alignment is "Against" and the bill fails). The process of finding what …

Solving Chromatic Number With Quantum Search And Quantum Counting, David Lutze

Master's Theses

This thesis presents a novel quantum algorithm that solves the Chromatic Number problem. Complexity analysis of this algorithm revealed a run time of O(2^n/2n²(log2n)²). This is an improvement over the best known algorithm, with a run time of 2ⁿn^O(1) [1]. This algorithm uses the Quantum Search algorithm (often called Grover's Algorithm), and the Quantum Counting algorithm. Chromatic Number is an example of an NP-Hard problem, which suggests that other NP-Hard problems can also benefit from a speed-up provided by quantum technology. This has wide implications as many real world problems can …

Modeling And Solving The Outsourcing Risk Management Problem In Multi-Echelon Supply Chains, Arian A. Nahangi

Master's Theses

Worldwide globalization has made supply chains more vulnerable to risk factors, increasing the associated costs of outsourcing goods. Outsourcing is highly beneficial for any company that values building upon its core competencies, but the emergence of the COVID-19 pandemic and other crises have exposed significant vulnerabilities within supply chains. These disruptions forced a shift in the production of goods from outsourcing to domestic methods.

This paper considers a multi-echelon supply chain model with global and domestic raw material suppliers, manufacturing plants, warehouses, and markets. All levels within the supply chain network are evaluated from a holistic perspective, calculating a total …

Design And Implementation Of A Deterministic And Nondeterministic Finite Automaton Simulator, Camron C. Dennler

Computer Science and Software Engineering

The purpose of this project is to assist students in visualizing and understanding the structure and operation of deterministic and nondeterministic finite automata. This software achieves this purpose by providing students with the ability to build, modify, and test automata in an intuitive environment. This enables a simple and efficient avenue for experimentation, which upholds the Cal Poly ideal of Learning by Doing.

Readers of this report should be familiar with basic concepts in the theory of finite state machines; a general understanding of object-oriented programming is also necessary.

Quantum Random Walk Search And Grover's Algorithm - An Introduction And Neutral-Atom Approach, Anna Maria Houk

Physics

In the sub-field of quantum algorithms, physicists and computer scientist take classical computing algorithms and principles and see if there is a more efficient or faster approach implementable on a quantum computer, i.e. a ”quantum advantage”. We take random walks, a widely applicable group of classical algorithms, and move them into the quantum computing paradigm. Additionally, an introduction to a popular quantum search algorithm called Grover’s search is included to guide the reader to the development of a quantum search algorithm using quantum random walks. To close the gap between algorithm and hardware, we will look at using neutral-atom (also …

Neural Network Pruning For Ecg Arrhythmia Classification, Isaac E. Labarge

Master's Theses

Convolutional Neural Networks (CNNs) are a widely accepted means of solving complex classification and detection problems in imaging and speech. However, problem complexity often leads to considerable increases in computation and parameter storage costs. Many successful attempts have been made in effectively reducing these overheads by pruning and compressing large CNNs with only a slight decline in model accuracy. In this study, two pruning methods are implemented and compared on the CIFAR-10 database and an ECG arrhythmia classification task. Each pruning method employs a pruning phase interleaved with a finetuning phase. It is shown that when performing the scale-factor pruning …

Grammar-Based Procedurally Generated Village Creation Tool, Kevin Matthew Graves

Computer Engineering

This project is a 3D village generator tool for Unity. It consists of three components: a building, mountain, and river generator. All of these generators use grammar-based procedural generation in order to create a unique and logical village and landscape each time the program is run.

Dish: Democracy In State Houses, Nicholas A. Russo

Master's Theses

In our current political climate, state level legislators have become increasingly impor- tant. Due to cuts in funding and growing focus at the national level, public oversight for these legislators has drastically decreased. This makes it difficult for citizens and activists to understand the relationships and commonalities between legislators. This thesis provides three contributions to address this issue. First, we created a data set containing over 1200 features focused on a legislator’s activity on bills. Second, we created embeddings that represented a legislator’s level of activity and engagement for a given bill using a custom model called Democracy2Vec. Third, we …

Finding Spanning Trees In Strongly Connected Graphs With Per-Vertex Degree Constraints, Samuel Benjamin Chase

Computer Science and Software Engineering

In this project, I sought to develop and prove new algorithms to create spanning trees on general graphs with per-vertex degree constraints. This means that each vertex in the graph would have some additional value, a degree constraint d. For a spanning tree to be correct, every vertex v_i in the spanning tree must have a degree exactly equal to a degree constraint d_i. This poses an additional constraint on what would otherwise be a trivial spanning tree problem. In this paper, two proofs related to my studies will be discussed and analyzed, leading to my algorithm …

The Effect Of Endgame Tablebases On Modern Chess Engines, Christopher D. Peterson

Computer Engineering

Modern chess engines have the ability to augment their evaluation by using massive tables containing billions of positions and their memorized solutions. This report examines the importance of these tables to better understand the circumstances under which they should be used. The analysis conducted in this paper empirically examines differences in size and speed of memorized positions and their impacts on engine strength. Using this technique, situations where memorized tables improve play (and situations where they do not) are discovered.