For a set O of n points in ${\mathbb{R}}^d$, the skyline consists of the subset of all points of O where no point is dominated by any other point of O. Suppose that each point $o_i\in O$ has an associated probability of existence $p_i\in (0,1]$. The problem of computing the skyline with the maximum probability of occurrence is considered. It is shown that in ${\mathbb{R}}^d$, $d\ge 3$, the problem is NP-hard and that the desired skyline cannot even be well-approximated in polynomial time unless $\mathit{P}=\mathit{NP}$. In ${\mathbb{R}}^2$, an optimal $\mathcal{O}(n\log n)$-time and $\mathcal{O}(n)$-space algorithm is given.

中文翻译：

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随机点最可能的天际线问题

对于一组Ø的ñ在点${\mathbb{[R}}^d$，天际线由O的所有点的子集组成，其中任何点都不受O的任何其他点支配。假设每个点${Ø}_{\mathrm{一世}}\in Ø$ 有相关的存在概率 $p_{\mathrm{一世}}\in （0，\mathrm{1个}]$。考虑了以最大发生概率计算天际线的问题。结果表明${\mathbb{[R}}^d$， $d\ge 3$，问题是NP难，并且除非在多项式时间内无法很好地逼近所需的天际线，否则 $\mathit{P}=\mathit{NP}$。在${\mathbb{[R}}^2$最佳 $\mathcal{Ø}（ñ\mathrm{日志}ñ）$-时间和 $\mathcal{Ø}（ñ）$给出了空间算法。