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An Efficient Algorithm for Decomposition of Partially Ordered Sets

Author

Listed:
  • Elsayed Badr
  • Mohamed EL-Hakeem
  • Enas E. El-Sharawy
  • Thowiba E. Ahmed
  • Mohammad W. Alomari

Abstract

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.

Suggested Citation

  • Elsayed Badr & Mohamed EL-Hakeem & Enas E. El-Sharawy & Thowiba E. Ahmed & Mohammad W. Alomari, 2023. "An Efficient Algorithm for Decomposition of Partially Ordered Sets," Journal of Mathematics, Hindawi, vol. 2023, pages 1-11, May.
    • Handle: RePEc:hin:jjmath:9920700
    DOI: 10.1155/2023/9920700
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