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The Sarkar-Wang algorithm computes the hat version of the Heegaard Floerhomology of a closed oriented three manifold. This paper analyzes thecomputational complexity of the Sarkar-Wang algorithm; then the algorithm ismodified to obtain a better bound. Then the computational complexity ofcalculating HFK hat from a Heegaard diagram by means of the modifiedSarkar-Wang algorithm is also analyzed. Under certain assumptions it is shownthat the modified Sarkar-Wang algorithm is faster than theManolescu-Ozsvath-Sarkar algorithm.

A Modification of the Sarkar-Wang Algorithm and an Analysis of its Computational Complexity