Abstract
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.
Highlights
Between 15% and 20% of the population suffers from some form of allergic contact dermatitis [26]
We show how to use our approximation algorithm for graphs specified in Theorem 1 to obtain a clustering with small average service time for directed hypergraphs
We introduce the problem of clustering vertices of a weighted hypergraph to minimize the average service time of its edges
Summary
Between 15% and 20% of the population suffers from some form of allergic contact dermatitis [26]. The study of this paper answers the question how to cluster different allergens together such that common anamnesis require a small number of patch tests. This is in order to reduce the cost and patient’s discomfort. We would like to construct the program such that attendees interested in particular topics can hear all talks on these topics by attending a small number of sessions Another application is in disk servers where one would like to cluster on the same server files that are often read together for minimizing the number of servers that have to be accessed
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