Before revision:  Also, we show that the smallest largest-area triangle can be found in O(n^2 \log n) time . As for finding smallest-area triangles, we show that finding the largest smallest-area triangle is NP-hard , but that the smallest possible area triangle for a set of arbitrary length parallel line segments can be found in O(n^2) time.
After revision:  Also, we show that the smallest largest-area triangle can be found in O(n^2 \log n) time ; maximizing the smallest triangle is NP-hard , but that the smallest possible area triangle for a set of arbitrary length parallel line segments can be found in O(n^2) time.