A polynomial-time solution for the maximum subsets problem
A polynomial-time solution for the maximum subsets problem
The main purpose of this paper is to determine a non-trivial tractable class of the maximum (k,m)-subsets problem. More specifically, we show that we can solve this problem in polynomial time for m = 1. Depending on the value of k with respect to n, we prove that in the best-case scenario our algorithm runs in O( √ n) time. On the other hand, an upper bound for solving it is given by O(n4/k3). Furthermore, for the case where n = k2, we design and implement an algorithm in Python that yields a solution in O(n5/2).
Algorithms, Discrete mathematics, Tractability
Challita, Khalil
d763f952-da59-4221-9fc7-265bfc9aa3d7
Abdo, Jacques Bou
aab9068d-4e81-4d07-863f-e977e53e50d4
Farhat, Hikmat
4b7583f4-d03c-425e-a65a-82c0e157e7e6
Makary, Mireille
98445f2a-b81b-423d-a24f-58e8f78150b6
2022
Challita, Khalil
d763f952-da59-4221-9fc7-265bfc9aa3d7
Abdo, Jacques Bou
aab9068d-4e81-4d07-863f-e977e53e50d4
Farhat, Hikmat
4b7583f4-d03c-425e-a65a-82c0e157e7e6
Makary, Mireille
98445f2a-b81b-423d-a24f-58e8f78150b6
Challita, Khalil, Abdo, Jacques Bou, Farhat, Hikmat and Makary, Mireille
(2022)
A polynomial-time solution for the maximum subsets problem.
IAENG International Journal of Computer Science, 49 (4), [IJCS_49_4_19].
Abstract
The main purpose of this paper is to determine a non-trivial tractable class of the maximum (k,m)-subsets problem. More specifically, we show that we can solve this problem in polynomial time for m = 1. Depending on the value of k with respect to n, we prove that in the best-case scenario our algorithm runs in O( √ n) time. On the other hand, an upper bound for solving it is given by O(n4/k3). Furthermore, for the case where n = k2, we design and implement an algorithm in Python that yields a solution in O(n5/2).
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Published date: 2022
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© 2022,IAENG International Journal of Computer Science. All Rights Reserved.
Keywords:
Algorithms, Discrete mathematics, Tractability
Identifiers
Local EPrints ID: 492313
URI: http://eprints.soton.ac.uk/id/eprint/492313
ISSN: 1819-656X
PURE UUID: 778513ab-2401-44fd-bd03-b08e342f552d
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Date deposited: 23 Jul 2024 17:13
Last modified: 24 Jul 2024 02:06
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Contributors
Author:
Khalil Challita
Author:
Jacques Bou Abdo
Author:
Hikmat Farhat
Author:
Mireille Makary
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