Before revision: In this paper we study the following problem: we are given a set of imprecise points modeled as parallel line segments  , and we wish to place a point on each line segment such that the resulting point set maximizes /minimizes the size of the largest /smallest area k-gon. We first study the problem for the case k=3. We show that for a given set of parallel line segments of equal length the largest possible area triangle can be found in O(n \log n) time , and for line segments of arbitrary length the problem can be solved in O(n ^2) time .
After revision: In this paper we study the following problem: we are given a set of imprecise points modeled as parallel line segments , and we wish to place a point on each line segment such that the resulting point set maximizes /minimizes the size of the largest or smallest triangle in the set. We analyze the complexity of the four resulting computational problems, and we show that three of them admit polynomial-time algorithms, while the fourth is NP-hard. Specifically, we show that maximizing the largest triangle can be found in O(n \log n) time , and for line segments of arbitrary length the problem can be solved in O(n ^2) time .