An Efficient Algorithm for Decomposition of Partially Ordered Sets

Efficient time complexities for partial ordered sets or posets are well-researched field. Hopcroft and Karp introduced an algorithm that solves the minimal chain decomposition in O (n2.5) time. Felsner et al. proposed an algorithm that reduces the time complexity to O (kn2) such that n is the number...

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Main Authors: Elsayed Badr, Mohamed EL-Hakeem, Enas E. El-Sharawy, Thowiba E. Ahmed
Format: Article
Language:English
Published: Wiley 2023-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2023/9920700
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author Elsayed Badr
Mohamed EL-Hakeem
Enas E. El-Sharawy
Thowiba E. Ahmed
author_facet Elsayed Badr
Mohamed EL-Hakeem
Enas E. El-Sharawy
Thowiba E. Ahmed
author_sort Elsayed Badr
collection DOAJ
description Efficient time complexities for partial ordered sets or posets are well-researched field. Hopcroft and Karp introduced an algorithm that solves the minimal chain decomposition in O (n2.5) time. Felsner et al. proposed an algorithm that reduces the time complexity to O (kn2) such that n is the number of elements of the poset and k is its width. The main goal of this paper is proposing an efficient algorithm to compute the width of a given partially ordered set P according to Dilworth’s theorem. It is an efficient and simple algorithm. The time complexity of this algorithm is O (kn), such that n is the number of elements of the partially ordered set P and k is the width of P. The computational results show that the proposed algorithm outperforms other related algorithms.
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institution DOAJ
issn 2314-4785
language English
publishDate 2023-01-01
publisher Wiley
record_format Article
series Journal of Mathematics
spelling doaj-art-95df26883c014707b0c445d2d2b6982b2025-08-20T03:20:33ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/9920700An Efficient Algorithm for Decomposition of Partially Ordered SetsElsayed Badr0Mohamed EL-Hakeem1Enas E. El-Sharawy2Thowiba E. Ahmed3Scientific Computing DepartmentArtificial Intelligence DepartmentComputer Science DepartmentComputer Science DepartmentEfficient time complexities for partial ordered sets or posets are well-researched field. Hopcroft and Karp introduced an algorithm that solves the minimal chain decomposition in O (n2.5) time. Felsner et al. proposed an algorithm that reduces the time complexity to O (kn2) such that n is the number of elements of the poset and k is its width. The main goal of this paper is proposing an efficient algorithm to compute the width of a given partially ordered set P according to Dilworth’s theorem. It is an efficient and simple algorithm. The time complexity of this algorithm is O (kn), such that n is the number of elements of the partially ordered set P and k is the width of P. The computational results show that the proposed algorithm outperforms other related algorithms.http://dx.doi.org/10.1155/2023/9920700
spellingShingle Elsayed Badr
Mohamed EL-Hakeem
Enas E. El-Sharawy
Thowiba E. Ahmed
An Efficient Algorithm for Decomposition of Partially Ordered Sets
Journal of Mathematics
title An Efficient Algorithm for Decomposition of Partially Ordered Sets
title_full An Efficient Algorithm for Decomposition of Partially Ordered Sets
title_fullStr An Efficient Algorithm for Decomposition of Partially Ordered Sets
title_full_unstemmed An Efficient Algorithm for Decomposition of Partially Ordered Sets
title_short An Efficient Algorithm for Decomposition of Partially Ordered Sets
title_sort efficient algorithm for decomposition of partially ordered sets
url http://dx.doi.org/10.1155/2023/9920700
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