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The Hammock(⏟𝟐, 𝟐 , … , 𝟐 / π’Œ )-Poset Cover Problem is a variation of the Poset Cover Problem with the same input – set {π‘³πŸ, π‘³πŸ, … , π‘³π’Ž} of linear orders over the set {𝟏, 𝟐, … ,𝒏}, but the solution is restricted to a set of simple hammock(𝟐⏟, 𝟐 , … , 𝟐 / π’Œ ) posets. The problem is NP-Hard when π’Œ β‰₯ πŸ‘ but is in 𝑷 when π’Œ = 𝟏. The computational complexity of the problem when π’Œ = 𝟐 is not yet known. In this paper, we determine the approximation complexity of the cases that have been shown to be NP-Hard. We show that the Hammock(𝟐⏟, 𝟐 , … , 𝟐 / π’Œ )-Poset Cover Problem is in APX and, in particular, (𝟏 + 𝟏/𝟐 π’Œ )-approximable, for π’Œ β‰₯ πŸ‘. On the other hand, we also explore the computational complexity for the case where π’Œ = 𝟐 [Hammock(2,2)-Poset Cover Problem]. We show that it is in 𝑷 when the transposition graph of the input set of linear orders is rectangular