- Author:
- Andrew C Yao
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.
Cited By
Ben-Or M Lower bounds for algebraic computation trees Proceedings of the fifteenth annual ACM symposium on Theory of computing, (80-86)- Bentley J, Preparata F and Faust M (1982). Approximation algorithms for convex hulls, Communications of the ACM, 25:1, (64-68), Online publication date: 1-Jan-1982.
- Overmars M and Leeuwen J Dynamically maintaining configurations in the plane (Detailed Abstract) Proceedings of the twelfth annual ACM symposium on Theory of computing, (135-145)
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