Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider a natural variation of the concept of stabbing a set of segments with a simple polygon: a segment s is stabbed by a simple polygon P if at least one endpoint of s is contained in P, and a segment set S is stabbed by P if P stabs every element of S. Given a segment set S,  study the problem of finding a simple polygon P stabbing S in a way that some measure of P (such as area or perimeter) is optimized.  show that if the elements of S are pairwise disjoint, the problem can be solved in polynomial time. In particular, this solves an open problem posed by Loffler and van Kreveld [Algorithmica 56(2), 236-269 (2010)] [16] about finding a maximum perimeter convex hull for a set of imprecise points modeled as line segments. Our algorithm can also be extended to work for a more general problem, in which instead of segments, the set S consists of a collection of point sets with pairwise disjoint convex hulls.  also prove that for general segments our stabbing problem is NP-hard.
['José Miguel Díaz-Báñez', 'Matias Korman', 'Pablo Pérez-Lantero', 'Alexander Pilz', 'Carlos Seara', 'Rodrigo I. Silveira']
I am writing a research paper on a idea New results on stabbing segments with a polygon
[{"from": "human", "value": "I am writing a research paper on a idea New results on stabbing segments with a polygon"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider a natural variation of the concept of stabbing a set of segments with a simple polygon: a segment s is stabbed by a simple polygon P if at least one endpoint of s is contained in P, and a segment set S is stabbed by P if P stabs every element of S. Given a segment set S,  study the problem of finding a simple polygon P stabbing S in a way that some measure of P (such as area or perimeter) is optimized.  show that if the elements of S are pairwise disjoint, the problem can be solved in polynomial time. In particular, this solves an open problem posed by Loffler and van Kreveld [Algorithmica 56(2), 236-269 (2010)] [16] about finding a maximum perimeter convex hull for a set of imprecise points modeled as line segments. Our algorithm can also be extended to work for a more general problem, in which instead of segments, the set S consists of a collection of point sets with pairwise disjoint convex hulls.  also prove that for general segments our stabbing problem is NP-hard."}]