  In a recent paper, the first author and his collaborator developed a method
to compute an upper bound of the dimension of instanton Floer homology via
Heegaard Diagrams of 3-manifolds. For a knot inside S3, we further develop an
algorithm that can compute an upper bound of the dimension of instanton knot
homology from knot diagrams. We test the effectiveness of the algorithm and
found that for all knots up to seven crossings, the algorithm provides sharp
bounds. In the second half of the paper, we show that, if the instanton knot
Floer homology of a knot has a specified form, then the knot must an instanton
L-space knot.
