Geometric Freeze-Tag Problem

We study the Freeze-Tag Problem (FTP), introduced by Arkin et al. (SODA'02), where the objective is to activate a group of n robots, starting from a single initially active robot. Robots are positioned in $\mathbb{R}^d$, and once activated, they move at a constant speed to wake up others. The goal is to minimize the time required to activate the last robot, known as the makespan. We establish new upper bounds for the makespan under the $l_1$ and $l_2$ norms in $\mathbb{R}^2$ and $\mathbb{R}^3$. Specifically, we improve the previous upper bound for $(\mathbb{R}^2, l_2)$ from $7.07r$ (Bonichon et al., DISC'24) to $5.064r$. For $(\mathbb{R}^3, l_1)$, we derive a makespan bound of $13r$, which translates to $22.52r$ for $(\mathbb{R}^3, l_2)$. Here, $r$ denotes the maximum distance of any robot from the initially active robot under the given norm. To our knowledge, these are the first makespan bounds for FTP in $\mathbb{R}^3$. Additionally, we show that the maximum makespan for $n$ robots is not necessarily achieved when robots are equally distributed along the boundary in $(\mathbb{R}^2, l_2)$. We further investigate FTP in $(\mathbb{R}^3, l_2)$ for specific configurations where robots lie on a boundary, providing insights into practical scenarios.

Utilizing ChatGPT in a Data Structures and Algorithms Course: A Teaching Assistant's Perspective

Integrating large language models (LLMs) like ChatGPT is revolutionizing the field of computer science education. These models offer new possibilities for enriching student learning and supporting teaching assistants (TAs) in providing prompt feedback and supplementary learning resources. This research delves into the use of ChatGPT in a data structures and algorithms (DSA) course, particularly when combined with TA supervision. The findings demonstrate that incorporating ChatGPT with structured prompts and active TA guidance enhances students' understanding of intricate algorithmic concepts, boosts engagement, and elevates academic performance. However, challenges exist in addressing academic integrity and the limitations of LLMs in tackling complex problems. The study underscores the importance of active TA involvement in reducing students' reliance on AI-generated content and amplifying the overall educational impact. The results suggest that while LLMs can be advantageous for education, their successful integration demands continuous oversight and a thoughtful balance between AI and human guidance.