Polynomial-Time Approximation Scheme for a Problem of Searching for the Largest Subset with the Constraint on Quadratic Variation
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The paper is addressed to one strongly NP-hard problem of searching for the largest subset in the finite set of points in Euclidean space. A restriction is imposed on the searched subset: quadratic variation of its points with respect to the unknown centroid of this subset must not exceed a given value. We present the first polynomial-time approximation scheme for this problem.
KeywordsEuclidean space Largest subset Quadratic variation NP-hard problem Polynomial-time approximation scheme
The study was supported by the Russian Foundation for Basic Research, projects 19-01-00308 and 18-31-00398, by the Russian Academy of Science (the Program of basic research), project 0314-2019-0015, and by the Russian Ministry of Science and Education under the 5-100 Excellence Programme.
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