Before revision:  We introduce an algorithm that produces a snapping fixture with such properties in O(n ^5) time , if a snapping fixture exists , and an efficient and robust implementation of this algorithm .
After revision:  We introduce an algorithm that produces a snapping fixture with such properties in O(n ^3) time that produces a snapping fixture, minimizing the number of fingers and optimizing additional objectives, if a snapping fixture exists , and an efficient and robust implementation of this algorithm .