کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
422161 685035 2008 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the Complexity of Convex Hulls of Subsets of the Two-Dimensional Plane
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
On the Complexity of Convex Hulls of Subsets of the Two-Dimensional Plane
چکیده انگلیسی

We investigate the computational complexity of computing the convex hull of a two-dimensional set. We study this problem in the polynomial-time complexity theory of real functions based on the oracle Turing machine model. We show that the convex hull of a two-dimensional Jordan domain S is not necessarily recursively recognizable even if S is polynomial-time recognizable. On the other hand, if the boundary of a Jordan domain S is polynomial-time computable, then the convex hull of S must be NP-recognizable, and it is not necessarily polynomial-time recognizable if P≠NP. We also show that the area of the convex hull of a Jordan domain S with a polynomial-time computable boundary can be computed in polynomial time relative to an oracle function in #P. On the other hand, whether the area itself is a #P real number depends on the open question of whether NP=UP.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Electronic Notes in Theoretical Computer Science - Volume 202, 21 March 2008, Pages 121-135