This paper proposes an efficient priority assignment algorithm for fixed priority preemption threshold scheduling (PTS), which we named FAST-TRAVERSE. It is optimal in the sense that it always finds a feasible priority assignment if one exists. While there are existing optimal algorithms, they are inefficient to be used in practice. The key ideas of FAST-TRAVERSE are to prune sibling traverses and preemption threshold assignments if possible based on the notion of the effective blocking task. The empirical evaluation results clearly show that FAST-TRAVERSE achieves the largest feasibility and can be employed as an on-line priority assignment algorithm for PTS.