A solution to the problem of clustered objects compact partitioning

The urgency of the study consists in the fact that an object arrangement topology of a distributed system is often nonuniform. Objects can be placed at different distances from each other, thus forming clusters. That is why solving the problem of compact partitioning into sets containing thousands of objects requires the most effective way to a better use of natural structuring of objects that form clusters. The aim of the study is the development of methods of compact partitioning of sets of objects presented as clusters. The research methods are based on applied theories of sets, theory of compact sets and compact partitions, and linear programming methods with Boolean variables. As a result, the paper offers the method necessary to analyze composition and content of clusters. It also evaluates cluster compactness, which results in the decision to include clusters into the sets of partitions. It addresses the problem of optimizing the rearrangement of objects between compact sets that form clusters, which is based on the criteria of maximizing the total compactness of sets. The problem is formulated in the class of objectives of linear programming methods with Boolean variables. It introduces the example of object rearrangement