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An approximation scheme for a problem of search for a vector subset

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Abstract

We consider the following clustering problem: Given a vector set, find a subset of cardinality k and minimum square deviation from its mean. The distance between the vectors is defined by the Euclideanmetric. We present an approximation scheme (PTAS) that allows us to solve this problem with an arbitrary relative error ɛ in time O(n 2/ɛ+1(9/ɛ)3/ɛ d), where n is the number of vectors of the input set and d denotes the dimension of the space.

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References

  1. A. V. Kel’manov and A. V. Pyatkin, “NP-Completeness of Some Problems of Choosing a Vector Subset,” Diskret. Anal. Issled. Oper. 17(5), 37–45 (2010) [J. Appl. Indust. Math. 5 (1), 352–357 (2011)].

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    V. V. Shenmaier

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  1. V. V. Shenmaier
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Correspondence to V. V. Shenmaier.

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Original Russian Text © V.V. Shenmaier, 2012, published in Diskretnyi Analiz i Issledovanie Operatsii, 2012, Vol. 19, No. 2, pp. 92–100.

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Shenmaier, V.V. An approximation scheme for a problem of search for a vector subset. J. Appl. Ind. Math. 6, 381–386 (2012). https://doi.org/10.1134/S1990478912030131

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  • DOI: https://doi.org/10.1134/S1990478912030131

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