Author: Kylind Reagan
This repository contains my implementations, experiments, and notes related to advanced algorithm design and analysis. The purpose is not only to provide working code for classical and modern algorithms, but also to document the reasoning, trade-offs, and performance considerations behind each approach.
Algorithms here span both theoretical foundations and practical applications in data science, optimization, and large-scale computation. My goal is to turn this into a long-term reference and resource as I deepen my understanding of the field.
Algorithms are the foundation of efficient problem solving across computer science and applied disciplines.
This repository reflects my effort to:
- Strengthen my theoretical foundation by studying advanced algorithmic ideas.
- Connect theory with practice by implementing and testing algorithms.
- Provide reusable, well-documented code for future projects in optimization, machine learning, and systems design.
- Document insights, learning outcomes, and open questions along the way.
- Implement advanced techniques: flow networks, approximation algorithms, streaming methods.
- Compare paradigms: deterministic vs. randomized, exact vs. approximate.
- Benchmark performance and scalability on synthetic + real-world data.
- Explore emerging directions: spectral graph theory, convex optimization, quantum computing.
- Build a structured, well-documented archive of algorithms and notes.
| Order | Topic |
|---|---|
| 1 | Advanced Trees and Heaps |
| 2 | Flow Networks Including potential near-linear solutions with Laplacian solvers |
| 3 | Linear Programming |
| 4 | Matrices in Advanced Algorithms Focus on Laplacian Matrices |
| 5 | Spectral Graph Theory |
| 6 | Sorting Networks |
| 7 | Number-Theoretic Algorithms |
| 8 | Approximation Algorithms |
| 9 | Randomization Techniques |
| 10 | Streaming Algorithms Sketching, heavy hitters, dimensionality reduction |
| 11 | Semidefinite Programming Applications to Max-Cut, Grothendieck inequality |
| 12 | Convex and Submodular Optimization Gradient methods, Lovász extensions, ML applications |
| 13 | Miscellaneous & Emerging Topics Online algorithms, fine-grained complexity, sublinear time |
- Clone the repository:
git clone https://github.com/kylindreagan/Senior-Study