Abstract
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 2𝒎 𝒏2 + 𝑶(�𝒌 𝒊 � 1 2𝒎𝒊𝒏) - exponential even for small fixed 𝒌.
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