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On finding minimum cardinality subset of vectors with a constraint on the sum of squared euclidean pairwise distances. / Eremeev, Anton V.; Kovalyov, Mikhail Y.; Pyatkin, Artem V.
Learning and Intelligent Optimization - 14th International Conference, LION 14, 2020, Revised Selected Papers. ed. / Ilias S. Kotsireas; Panos M. Pardalos. Springer Gabler, 2020. p. 40-45 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12096 LNCS).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
}
TY - GEN
T1 - On finding minimum cardinality subset of vectors with a constraint on the sum of squared euclidean pairwise distances
AU - Eremeev, Anton V.
AU - Kovalyov, Mikhail Y.
AU - Pyatkin, Artem V.
N1 - Publisher Copyright: © Springer Nature Switzerland AG 2020.
PY - 2020/7/1
Y1 - 2020/7/1
N2 - In this paper, we consider the problem of finding a minimum cardinality subset of vectors, given a constraint on the sum of squared Euclidean distances between all vectors of the chosen subset. This problem is closely related to the well-known Maximum Diversity Problem. The main difference consists in swapping the constraint with the optimization criterion. We prove that the problem is NP-hard in the strong sense. An exact algorithm for solving this problem is proposed. The algorithm has a pseudo-polynomial time complexity in the special case of the problem, where the dimension of the space is bounded from above by a constant and the input data are integer.
AB - In this paper, we consider the problem of finding a minimum cardinality subset of vectors, given a constraint on the sum of squared Euclidean distances between all vectors of the chosen subset. This problem is closely related to the well-known Maximum Diversity Problem. The main difference consists in swapping the constraint with the optimization criterion. We prove that the problem is NP-hard in the strong sense. An exact algorithm for solving this problem is proposed. The algorithm has a pseudo-polynomial time complexity in the special case of the problem, where the dimension of the space is bounded from above by a constant and the input data are integer.
KW - Euclidean space
KW - Exact algorithm
KW - Integer instance
KW - NP-hardness
KW - Pseudo-polynomial time
KW - Subset of points
UR - http://www.scopus.com/inward/record.url?scp=85089211896&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-53552-0_6
DO - 10.1007/978-3-030-53552-0_6
M3 - Conference contribution
AN - SCOPUS:85089211896
SN - 9783030535513
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 40
EP - 45
BT - Learning and Intelligent Optimization - 14th International Conference, LION 14, 2020, Revised Selected Papers
A2 - Kotsireas, Ilias S.
A2 - Pardalos, Panos M.
PB - Springer Gabler
T2 - 14th International Conference on Learning and Intelligent Optimization, LION 2020
Y2 - 24 May 2020 through 28 May 2020
ER -
ID: 24962158