  We present a braid-theoretic approach to combinatorially computing knot Floer
homology. To a knot or link K, which is braided about the standard disk open
book decomposition for (S^3,\xi_std), we associate a corresponding
multi-pointed nice Heegaard diagram. We then describe an explicit algorithm for
computing the associated knot Floer homology groups. We compute explicit bounds
for the computational complexity of our algorithm and demonstrate that, in many
cases, it is significantly faster than the previous approach using grid
diagrams.
