Research output: Contribution to journal › Article › peer-review
An Approximation Scheme for the Problem of Finding a Subsequence. / Kel’manov, A. V.; Romanchenko, S. M.; Khamidullin, S. A.
In: Numerical Analysis and Applications, Vol. 10, No. 4, 01.10.2017, p. 313-323.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - An Approximation Scheme for the Problem of Finding a Subsequence
AU - Kel’manov, A. V.
AU - Romanchenko, S. M.
AU - Khamidullin, S. A.
PY - 2017/10/1
Y1 - 2017/10/1
N2 - We consider a strongly NP-hard Euclidean problem of finding a subsequence in a finite sequence. The criterion of the solution is the minimum sum of squared distances from the elements of a sought subsequence to its geometric center (centroid). It is assumed that a sought subsequence contains a given number of elements. In addition, a sought subsequence should satisfy the following condition: the difference between the indices of each previous and subsequent points is bounded with given lower and upper constants.We present an approximation algorithm of solving the problem and prove that it is a fully polynomial-time approximation scheme (FPTAS) when the space dimension is bounded by a constant.
AB - We consider a strongly NP-hard Euclidean problem of finding a subsequence in a finite sequence. The criterion of the solution is the minimum sum of squared distances from the elements of a sought subsequence to its geometric center (centroid). It is assumed that a sought subsequence contains a given number of elements. In addition, a sought subsequence should satisfy the following condition: the difference between the indices of each previous and subsequent points is bounded with given lower and upper constants.We present an approximation algorithm of solving the problem and prove that it is a fully polynomial-time approximation scheme (FPTAS) when the space dimension is bounded by a constant.
KW - Euclidean space
KW - FPTAS
KW - minimum sum of squared distances
KW - NP-hardness
KW - sequence
UR - http://www.scopus.com/inward/record.url?scp=85042695119&partnerID=8YFLogxK
U2 - 10.1134/S1995423917040036
DO - 10.1134/S1995423917040036
M3 - Article
AN - SCOPUS:85042695119
VL - 10
SP - 313
EP - 323
JO - Numerical Analysis and Applications
JF - Numerical Analysis and Applications
SN - 1995-4239
IS - 4
ER -
ID: 10342626