Parameterized Algorithm for the Poset Cover Problem
It is already known that the 1-Poset and 2-Poset Cover Problems are in P. In this paper, we extended the previous results and devised an algorithm for the k-Poset Cover Problem, for any k number of posets that cover the input. The algorithm runs in O(m2k n2), where m and n are the input size. With t...
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| Main Authors: | , , , , |
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| Format: | text |
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Archīum Ateneo
2024
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| Subjects: | |
| Online Access: | https://archium.ateneo.edu/discs-faculty-pubs/410 https://archium.ateneo.edu/context/discs-faculty-pubs/article/1410/viewcontent/parameterized_algorithm_for_the_Poset_cover_problem_.pdf |
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| Institution: | Ateneo De Manila University |
| Summary: | It is already known that the 1-Poset and 2-Poset Cover Problems are in P. In this paper, we extended the previous results and devised an algorithm for the k-Poset Cover Problem, for any k number of posets that cover the input. The algorithm runs in O(m2k n2), where m and n are the input size. With this running time, we can say that the problem belongs to XP (slicewise polynomial). The algorithm runs efficiently for small fixed k but runs exponentially for large k. While the algorithm running time has yet not to be efficient for large k, we have shown a significant improvement from a brute-force solution, which runs in (Formula Presented) exponential even for small fixed k. |
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