arXiv subjects

Connor Phillips

Publications and source records attributed to Connor Phillips.

3 recordsLinked to original sources

arXiv2026

A Comprehensive Study of Clique Graphs and Clique Regular Graphs

If $\Gamma$ is a graph for which every edge is in exactly one clique of order $\omega$, then one can form a new graph with vertex set equal to these cliques. This is a generalization of the line graph of $\Gamma$. We discover many general results and classifications related to these clique graphs that will be useful to researchers studying graphs with this property. In particular, we find bounds on the spectrum of $\Gamma$ (with exact results when $\Gamma$ is $k$-regular) and some complete classifications when $\Gamma$ is strongly regular. We apply our results to derive novel information about the existence questions of certain strongly regular graphs. We also examine the critical group of graphs with this property and their associated transformations. Finally, we discuss examples of widely studied families of graphs that have this property, and provide some examples to make the results more concrete.

math.CO↗

arXiv2025

Accelerating a Linear Programming Algorithm on AMD GPUs

Linear Programming (LP) is a foundational optimization technique with widespread applications in finance, energy trading, and supply chain logistics. However, traditional Central Processing Unit (CPU)-based LP solvers often struggle to meet the latency and scalability demands of dynamic, high-dimensional industrial environments, creating a significant computational challenge. This project addresses these limitations by accelerating linear programming on AMD Graphics Processing Units (GPUs), leveraging the ROCm open-source platform and PyTorch. The core of this work is the development of a robust, high-performance, open-source implementation of the Primal-Dual Hybrid Gradient (PDHG) algorithm, engineered specifically for general LP problems on AMD hardware. Performance is evaluated against standard LP test sets and established CPU-based solvers, with a particular focus on challenging real- world instances including the Security-Constrained Economic Dispatch (SCED) to guide hyperparameter tuning. Our results show a significant improvement, with up to a 36x speedup on GPU over CPU for large-scale problems, highlighting the advantages of GPU acceleration in solving complex optimization tasks.

math.OC↗

arXiv2024

Navigating LLM Ethics: Advancements, Challenges, and Future Directions

This study addresses ethical issues surrounding Large Language Models (LLMs) within the field of artificial intelligence. It explores the common ethical challenges posed by both LLMs and other AI systems, such as privacy and fairness, as well as ethical challenges uniquely arising from LLMs. It highlights challenges such as hallucination, verifiable accountability, and decoding censorship complexity, which are unique to LLMs and distinct from those encountered in traditional AI systems. The study underscores the need to tackle these complexities to ensure accountability, reduce biases, and enhance transparency in the influential role that LLMs play in shaping information dissemination. It proposes mitigation strategies and future directions for LLM ethics, advocating for interdisciplinary collaboration. It recommends ethical frameworks tailored to specific domains and dynamic auditing systems adapted to diverse contexts. This roadmap aims to guide responsible development and integration of LLMs, envisioning a future where ethical considerations govern AI advancements in society.

cs.CY↗