Recently, large language models (LLMs) have demonstrated remarkable capabilities in understanding and generating natural language content, attracting widespread attention in both industry and academia. An increasing number of services offer LLMs for various tasks via APIs. Different LLMs demonstrate expertise in different domains of queries (e.g., text classification queries). Meanwhile, LLMs of different scales, complexities, and performance are priced diversely. Driven by this, several researchers are investigating strategies for selecting an ensemble of LLMs, aiming to decrease overall usage costs while enhancing performance. However, to our best knowledge, none of the existing works addresses the problem, how to find an LLM ensemble subject to a cost budget, which maximizes the ensemble performance with guarantees. In this paper, we formalize the performance of an ensemble of models (LLMs) using the notion of correctness probability, which we formally define. We develop an approach for aggregating responses from multiple LLMs to enhance ensemble performance. Building on this, we formulate the Optimal Ensemble Selection (OES) problem of selecting a set of LLMs subject to a cost budget that maximizes the overall correctness probability. We show that the correctness probability function is non-decreasing and non-submodular and provide evidence that the OES problem is likely to be NP-hard. By leveraging a submodular function that upper bounds correctness probability, we develop an algorithm, ThriftLLM, and prove that it achieves an instance-dependent approximation guarantee with high probability. Our framework functions as a data processing system that selects appropriate LLM operators to deliver high-quality results under budget constraints. It achieves state-of-the-art performance for text classification and entity matching queries on multiple real-world datasets against various baselines in our extensive experimental evaluation, while using a relatively lower cost budget, strongly supporting the effectiveness and superiority of our method.

Law enforcement and domain experts can detect human trafficking (HT) in online escort websites by analyzing suspicious clusters of connected ads. How can we explain clustering results intuitively and interactively, visualizing potential evidence for experts to analyze? We present TRAFFICVIS, the first interface for cluster-level HT detection and labeling. Developed through months of participatory design with domain experts, TRAFFICVIS provides coordinated views in conjunction with carefully chosen backend algorithms to effectively show spatio-temporal and text patterns to a wide variety of anti-HT stakeholders. We build upon state-of-the-art text clustering algorithms by incorporating shared metadata as a signal of connected and possibly suspicious activity, then visualize the results. Domain experts can use TRAFFICVIS to label clusters as HT, or other, suspicious, but non-HT activity such as spam and scam, quickly creating labeled datasets to enable further HT research. Through domain expert feedback and a usage scenario, we demonstrate TRAFFICVIS's efficacy. The feedback was overwhelmingly positive, with repeated high praises for the usability and explainability of our tool, the latter being vital for indicting possible criminals.