Tight Bounds on the Complexity of Recognizing Odd-Ranked Elements
Abstract
Let S = <s1, s2, s3, ..., sn> 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 si in S such that si is less than or equal to z. We consider the following decision problem: determine whether the odd-numbered elements s1, s3, s5, ... 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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