School of Engineering Department of Computer Science and Engineering 112 Open Topic in Algorithms and Complexity Supervisor: KAFSHDAR GOHARSHADY Amir / CSE Student: HASAN Dewan Saadman / DSCT Course: UROP 1000, Summer Given a graph where every vertex is assigned a non-negative weight, Weighted Independent Set problem asks to find the maximum weight of an independent set in . This problem can be solved in polynomial time in certain type of graphs, such as trees, grids using dynamic programming. Since the weighted independent set problem is NP-Hard, we combine the idea of dynamic programming and tree decomposition to provide an efficient solution to the problem. Given a graph with vertices and its tree decomposition of width at most , we show an algorithm that solves the problem in time 2 ∙ (1) ∙ . Open Topic in Algorithms and Complexity Supervisor: KAFSHDAR GOHARSHADY Amir / CSE Student: TSE Yik Long / QFIN Course: UROP 1100, Summer Parameterized algorithms refer to algorithms that solve a particular problem with one or more extra parameters that put constraints on the problem. This technique is particularly useful for problems which have no known polynomial algorithms (for instance, NP-hard problems), because it gives algorithms that depend polynomially on the extra parameter(s). In this paper, the basic concepts and techniques related to parameterization will be explored, which will be further illustrated using a well-known NP-hard problem, VERTEX COVER. Making Large Language Models (LLMs) Interact with Physical World Supervisor: LI Mo / CSE Student: LIANG Fangzhou / COMP YEUNG Wun Lam / CPEG Course: UROP 1100, Summer UROP 1100, Summer Human activity recognition (HAR) is an impactful research area with applications spanning healthcare, sports, and beyond. Traditional machine learning models and deep learning algorithms have achieved decent performance on HAR. However, these approaches typically require large amounts of labeled data for training, which limits their viability in scenarios with scarce labeled data. With the rise of Large Language models (LLMs), this paper explores the potential of using LLMs for zero-shot human activity classification to address the limitation of labeled data. Experiments on IMU time series datasets evaluate the performance of GPT4o-mini, benchmarking it against baseline models. Results showed that while current advanced LLMs have a limited understanding of raw sensor data, they show potential for classifying groups with distinguishable patterns.
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