Efficient Parallel Convex Hull Algorithms
IEEE Transactions on Computers
Mesh Computer Algorithms for Computational Geometry
IEEE Transactions on Computers
A Lower Bound to Finding Convex Hulls
Journal of the ACM (JACM)
Approximation algorithms for convex hulls
Communications of the ACM
Dynamically maintaining configurations in the plane (Detailed Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Fast approximation of convex hull
ACST'06 Proceedings of the 2nd IASTED international conference on Advances in computer science and technology
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Given a set S of n distinct points {($x_i$,$y_i$) | 0 $\leq$ i n}, the convex hull problem is to determine the vertices of the convex hull H(S). All the known algorithms for solving this problem have a worst-case running time of cn log n or higher, and employ only quadratic tests, i.e., tests of the form f($x_0$, $y_0$, $x_1$, $y_1$,...,$x_{n-1}$, $y_{n-1}$): 0 with f being any polynomial of degree not exceeding 2. In this paper, we show that any algorithm in the quadratic decision-tree model must make cn log n tests for some input.