Tight Bounds on the Complexity of Recognizing Odd-Ranked Elements
Computational Complexity
2007-05-23 v1 Data Structures and Algorithms
Abstract
Let S = <s_1, s_2, s_3, ..., s_n> be a given vector of n real numbers. The rank of a real z with respect to S is defined as the number of elements s_i in S such that s_i is less than or equal to z. We consider the following decision problem: determine whether the odd-numbered elements s_1, s_3, s_5, ... are precisely the elements of S whose rank with respect to S is odd. We prove a bound of Theta(n log n) on the number of operations required to solve this problem in the algebraic computation tree model.
Cite
@article{arxiv.cs/0606038,
title = {Tight Bounds on the Complexity of Recognizing Odd-Ranked Elements},
author = {Shripad Thite},
journal= {arXiv preprint arXiv:cs/0606038},
year = {2007}
}
Comments
3 pages