Detecting text generated by large language models (LLMs) is of great recent interest.

In this paper, we present a comprehensive study of the performance of average-link in metric spaces, regarding several natural criteria that capture separability and cohesion, and aremore interpretable than Dasgupta'scost function and itsvariants.

Our main result is a matching upper and lower bound for the secretary ranking problem.

In the most general setting, a coreset compresses the data set in such a way that for any set of previously specified candidate queries, the cost of evaluating the query and the cost of the coreset are similar,up to an arbitrarysmalldistortion. A popular subject in coreset literature is the Euclideank-means problem.