1) Relative to one another, how computable are the various knot homology theories? For example, how many crossings can we allow a knot and still hope to compute its Khovanov homology, versus its knot Floer or Khovanov-Rozansky homologies? (The latter two seem to be generally unlisted at the Atlas; KF at least has a page about how it can be computed, but KR seems totally absent. If I'm just not seeing the right link, feel free to let me know)

2) Do the algorithms by which these invariants are computed share common features, or are they really very specific to the particular homology being computed?

For example, people computing KF homology draw square pictures that look very different from the pictures drawn by people doing Khovanov homology. On a less superficial level, KF algorithms (as far as I can tell) appear to be 'global' in an essential way, while Khovanov calculations can be done locally, breaking a knot into smaller pieces and then working with the pieces. So I'm led to believe the computations involved are different in a really fundamental way, but would be interested to see some combinatorial connection (as opposed to a topological relationship). I have no idea how KR homology is computed, so have no idea how closely related the computations involved are to, say, ordinary Khovanov homology.