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In this paper, we prove that the Max Morse Matching Problem is approximable, thus resolving an open problem posed by Joswig and Pfetsch [1] . For D -dimensional simplicial complexes, we obtain a ( D + 1 ) ( D 2 + D + 1 ) -factor approximation ratio using a simple edge reorientation algorithm that removes cycles. For D ≥ 5 , we describe a 2 D -factor approximation algorithm for simplicial manifolds by processing the simplices in increasing order of dimension. This algorithm leads to 1 2 -factor approximation for 3-manifolds and 4 9 -factor approximation for 4-manifolds. This algorithm may also be applied to non-manifolds resulting in a 1 ( D + 1 ) -factor approximation ratio. One application of these algorithms is towards efficient homology computation of simplicial complexes. Experiments using a prototype implementation on several datasets indicate that the algorithm computes near optimal results. [ABSTRACT FROM AUTHOR]