O（n ^ 2）的渐近下界
[英]Asymptotic lower bound of O(n^2)
问题描述
Are there problems in P that have a proven asymptotic lower bound of O(n^2) or higher? 
P中是否存在已证明渐近下界为O（n ^ 2）或更高的问题？ (n is the number of bits a problem instance can be represented by). （n是问题实例可以表示的位数）。 This is not a homework question, just curiosity. 这不是一个作业问题，只是好奇心。
2 个解决方案
解决方案1
6 已采纳 2013-06-22 19:12:31
Yes, the time hierarchy theorem implies the existence of such problems. 是的， 时间层次定理意味着存在此类问题。 They're arguably not natural because they involve diagonalizing over all O(n^2)-time algorithms. 可以说它们是不自然的，因为它们涉及对所有O（n ^ 2）时间算法的对角化。
解决方案2
2 2013-06-23 08:35:23
3SUM comes to mind. 我想到了3SUM 。 There's a quadratic lower bound known for a certain linear decision-tree model due to Jeff Erickson. 由于杰夫·埃里克森（Jeff Erickson），对于某个线性决策树模型，存在一个已知的二次下界 。 (There are some barely-subquadratic algorithms for 3SUM in the literature for various models of computation. But I haven't looked at them and I don't know how they work.) （文献中针对各种计算模型存在一些3SUM的几乎次二次算法。但是我没有研究它们，也不知道它们是如何工作的。）
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