We study the problem of clustering the vertices of a weighted hypergraph such that on average the vertices of each edge can be covered by a small number of clusters. This problem has many applications, such as for designing medical tests, clustering files on disk servers, and placing network services on servers. The edges of the hypergraph model groups of items that are likely to be needed together, and the optimization criteria that we use can be interpreted as the average delay (or cost) to serve the items of a typical edge. We describe and analyze algorithms for this problem for the case in which the clusters have to be disjoint and for the case where clusters can overlap. The analysis is often subtle and reveals interesting structure and invariants that one can utilize.
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A preliminary version of this article was presented at the European Symposium on Algorithms (ESA), Vienna, Austria, September 2017. The work of O. Rottenstriech was partially supported by the Taub Family Foundation, as well as by the Technion Hiroshi Fujiwara Cyber Security Research Center and the Israel National Cyber Directorate, by the Alon fellowship, by German-Israeli Science Foundation (GIF) Young Scientists Program, and by the Gordon Fund for System Engineering. The work of H. Kaplan was partially supported by Israel Science Foundation (ISF) grant 1595/19 and by grants 1367/2016 from the German-Israeli Science Foundation (GIF). The work of A. Hassidim was partially supported by Israel Science Foundation (ISF) grant 1394/16. Authors’ addresses: O. Rottenstreich, Technion, Technion city, Haifa 3200003, Israel; email: email@example.com; H. Kaplan, Tel Aviv University, Ramat Aviv 6997801, Tel Aviv Israel; email: firstname.lastname@example.org; A. Hassidim, Bar-Ilan University, Ramat Gan, 5290002, Israel, and Google, Tel Aviv, Israel; email: email@example.com. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from firstname.lastname@example.org. © 2020 Association for Computing Machinery. 1549-6325/2020/05-ART40 $15.00 https://doi.org/10.1145/3386121
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