平均事例复杂度的统计学研究
A Statistical Peek into Average Case Complexity
摘要：
本文给出了一个统计冒险探索平均情况下的复杂性行为的计算机算法。而不是按照传统的计数为基础的分析（笔和纸）的方法，我们反而谈论的重量为基础的分析，允许不同的操作混合到一个概念上的界限称为统计界和它的经验估计，所谓的“经验O”。基于对所得结果的仔细分析，我们在算法分析领域中引入了两个新的结构。当遇到不存在期望值的数据模型（如本文所研究的连续输入数据和某些离散分布输入的柯西分布）时，平均案例分析的分析方法就显得苍白无力。我们的方法的实证方面，在计算机实验和应用统计学的推力在其范式，借着赞美和补充其理论对应的帮助之手。计算机科学也是或至少具有实验科学的方面，因此希望我们的统计发现也能在理论科学家中得到同样的认可。
英文摘要：
The present paper gives a statistical adventure towards exploring the average case complexity behavior of computer algorithms. Rather than following the traditional count based analytical (pen and paper) approach, we instead talk in terms of the weight based analysis that permits mixing of distinct operations into a conceptual bound called the statistical bound and its empirical estimate, the so called "empirical O". Based on careful analysis of the results obtained, we have introduced two new conjectures in the domain of algorithmic analysis. The analytical way of average case analysis falls flat when it comes to a data model for which the expectation does not exist (e.g. Cauchy distribution for continuous input data and certain discrete distribution inputs as those studied in the paper). The empirical side of our approach, with a thrust in computer experiments and applied statistics in its paradigm, lends a helping hand by complimenting and supplementing its theoretical counterpart. Computer science is or at least has aspects of an experimental science as well, and hence hopefully, our statistical findings will be equally recognized among theoretical scientists as well.
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