提出一种估计n个d维向量中最大向量平均个数的方法。该方法通过分析单个向量与其他向量子集的支配关系,求出最大向量平均个数的解析式。证明解析式满足已知的递归关系,得到最大向量平均个数的近似估计。与已有方法相比,该方法可应用到估计k个其他向量支配的平均个数问题。
A new method is proposed for estimating the average number of maxima in a set of n vectors in d-dimensional space.The new method reveals the probability that a vector is dominated by a set of other vectors,and obtains the analytic form of the average number of the maxima.After the fact that the analytic form satisfies a known recurrence is proved,the estimation of the average number can be derived naturally.Compared with the existed methods,the new method can be extended to the general problem of estimating the average number of the vectors that are only dominated by other k vectors.