Abstract
In this paper, we investigate algorithms for finding centers of a given collection \(\mathcal N\) of sets. In particular, we focus on metric rational set similarities, a broad class of similarity measures including Jaccard and Hamming. A rational set similarity S is called metric if \(D=1-S\) is a distance function. We study the 1-center problem on these metric spaces. The problem consists of finding a set C that minimizes the maximum distance of C to any set of \(\mathcal N\). We present a general framework that computes a \((1+\varepsilon )\) approximation for any metric rational set similarity.
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