Standard
Easy NP-hardness Proofs of Some Subset Choice Problems. / Pyatkin, Artem V.
Mathematical Optimization Theory and Operations Research - 19th International Conference, MOTOR 2020, Revised Selected Papers. ed. / Yury Kochetov; Igor Bykadorov; Tatiana Gruzdeva. Springer Science and Business Media Deutschland GmbH, 2020. p. 70-79 (Communications in Computer and Information Science; Vol. 1275 CCIS).
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
Harvard
Pyatkin, AV 2020,
Easy NP-hardness Proofs of Some Subset Choice Problems. in Y Kochetov, I Bykadorov & T Gruzdeva (eds),
Mathematical Optimization Theory and Operations Research - 19th International Conference, MOTOR 2020, Revised Selected Papers. Communications in Computer and Information Science, vol. 1275 CCIS, Springer Science and Business Media Deutschland GmbH, pp. 70-79, 19th International Conference on Mathematical Optimization Theory and Operations Research,MOTOR 2020, Novosibirsk, Russian Federation,
06.07.2020.
https://doi.org/10.1007/978-3-030-58657-7_8
APA
Vancouver
Pyatkin AV.
Easy NP-hardness Proofs of Some Subset Choice Problems. In Kochetov Y, Bykadorov I, Gruzdeva T, editors, Mathematical Optimization Theory and Operations Research - 19th International Conference, MOTOR 2020, Revised Selected Papers. Springer Science and Business Media Deutschland GmbH. 2020. p. 70-79. (Communications in Computer and Information Science). doi: 10.1007/978-3-030-58657-7_8
Author
Pyatkin, Artem V. /
Easy NP-hardness Proofs of Some Subset Choice Problems. Mathematical Optimization Theory and Operations Research - 19th International Conference, MOTOR 2020, Revised Selected Papers. editor / Yury Kochetov ; Igor Bykadorov ; Tatiana Gruzdeva. Springer Science and Business Media Deutschland GmbH, 2020. pp. 70-79 (Communications in Computer and Information Science).
BibTeX
@inproceedings{a7c55f74547c4c1592a0289cdbf4efba,
title = "Easy NP-hardness Proofs of Some Subset Choice Problems",
abstract = "We consider the following subset choice problems: given a family of Euclidean vectors, find a subset having the largest a) norm of the sum of its elements; b) square of the norm of the sum of its elements divided by the cardinality of the subset. The NP-hardness of these problems was proved in two papers about ten years ago by reduction of 3-SAT problem. However, that proofs were very tedious and hard to read. In the current paper much easier and natural proofs are presented.",
keywords = "2-partition, Clustering, Euclidean space, Strong np-hardness, Subset choice",
author = "Pyatkin, {Artem V.}",
year = "2020",
month = jul,
doi = "10.1007/978-3-030-58657-7_8",
language = "English",
isbn = "9783030586560",
series = "Communications in Computer and Information Science",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "70--79",
editor = "Yury Kochetov and Igor Bykadorov and Tatiana Gruzdeva",
booktitle = "Mathematical Optimization Theory and Operations Research - 19th International Conference, MOTOR 2020, Revised Selected Papers",
address = "Germany",
note = "19th International Conference on Mathematical Optimization Theory and Operations Research,MOTOR 2020 ; Conference date: 06-07-2020 Through 10-07-2020",
}
RIS
TY - GEN
T1 - Easy NP-hardness Proofs of Some Subset Choice Problems
AU - Pyatkin, Artem V.
PY - 2020/7
Y1 - 2020/7
N2 - We consider the following subset choice problems: given a family of Euclidean vectors, find a subset having the largest a) norm of the sum of its elements; b) square of the norm of the sum of its elements divided by the cardinality of the subset. The NP-hardness of these problems was proved in two papers about ten years ago by reduction of 3-SAT problem. However, that proofs were very tedious and hard to read. In the current paper much easier and natural proofs are presented.
AB - We consider the following subset choice problems: given a family of Euclidean vectors, find a subset having the largest a) norm of the sum of its elements; b) square of the norm of the sum of its elements divided by the cardinality of the subset. The NP-hardness of these problems was proved in two papers about ten years ago by reduction of 3-SAT problem. However, that proofs were very tedious and hard to read. In the current paper much easier and natural proofs are presented.
KW - 2-partition
KW - Clustering
KW - Euclidean space
KW - Strong np-hardness
KW - Subset choice
UR - http://www.scopus.com/inward/record.url?scp=85092118819&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-58657-7_8
DO - 10.1007/978-3-030-58657-7_8
M3 - Conference contribution
AN - SCOPUS:85092118819
SN - 9783030586560
T3 - Communications in Computer and Information Science
SP - 70
EP - 79
BT - Mathematical Optimization Theory and Operations Research - 19th International Conference, MOTOR 2020, Revised Selected Papers
A2 - Kochetov, Yury
A2 - Bykadorov, Igor
A2 - Gruzdeva, Tatiana
PB - Springer Science and Business Media Deutschland GmbH
T2 - 19th International Conference on Mathematical Optimization Theory and Operations Research,MOTOR 2020
Y2 - 6 July 2020 through 10 July 2020
ER -
