Tight Bounds on the Complexity of Recognizing Odd-Ranked Elements

Shripad Thite

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Tight Bounds on the Complexity of Recognizing Odd-Ranked Elements

Shripad Thite

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Abstract

Let S = 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.

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Shripad Thite. 2006-06-08. Tight Bounds on the Complexity of Recognizing Odd-Ranked Elements. https://arxiv.org/abs/cs/0606038

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