奇数阶元素识别复杂性的紧界
Tight Bounds on the Complexity of Recognizing Odd-Ranked Elements
摘要：
令S = <s_1，s_2，s_3，.，s_n>是n个实数的给定向量。实数z相对于S的秩被定义为S中元素s_i的数量，使得s_i小于或等于z。我们考虑以下决策问题：确定奇数元素s_1，s_3，s_5，.恰好是S中秩为奇数的元素。我们证明了在代数计算树模型中解决这个问题所需的操作数上的Theta（n log n）的界。
英文摘要：
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.
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