  The Sarkar-Wang algorithm computes the hat version of the Heegaard Floer
homology of a closed oriented three manifold. This paper analyzes the
computational complexity of the Sarkar-Wang algorithm; then the algorithm is
modified to obtain a better bound. Then the computational complexity of
calculating HFK hat from a Heegaard diagram by means of the modified
Sarkar-Wang algorithm is also analyzed. Under certain assumptions it is shown
that the modified Sarkar-Wang algorithm is faster than the
Manolescu-Ozsvath-Sarkar algorithm.
