  We describe an algorithm to find ribbon disks for alternating knots, and the
results of a computer implementation of this algorithm. The algorithm is
underlain by a slice link obstruction coming from Donaldson's diagonalisation
theorem. It successfully finds ribbon disks for slice two-bridge knots and for
the connected sum of any alternating knot with its reverse mirror, as well as
for 81,560 prime alternating knots of 19 or fewer crossings. We also identify
some examples of ribbon alternating knots for which the algorithm fails to find
ribbon disks.
