  Measurement based quantum computation is a quantum computing paradigm, that
employs single-qubit measurements performed on an entangled resource state in
the form of a cluster state. A basic ingredient in the construction of the
resource state is the type II fusion procedure, which connects two cluster
states. We generalize the type II fusion procedure by generalizing the fusion
matrix, and classify the resulting final states, which also include cluster
states up to single-qubit rotations. We prove that the probability for the
success of the generalized type II fusion is bounded by fifty percent, and
classify all the possibilities to saturate the bound. We analyze the
enhancement of the fusion success probability above the fifty percent bound, by
the reduction of the entanglement entropy of the fusion link. We prove that the
only states, that can be obtained with hundred percent probability of success,
are product states.
