The skyline of a set P of points consists of the “best” points with respect to minimization or maximization of the attribute values. A point p dominates another point q if p is as good as q in all dimensions and it is strictly better than q in at least one dimension. In this work, we focus on the 2-d space and provide expected performance guarantees for dynamic (insertions and deletions) 3-sided range skyline queries. We assume that the x and y coordinates of the points are drawn from a class of distributions and present the ML-tree (Modified Layered Range-tree), which attains $O({\log }^{2}N\log \log N)$ expected update time and $O(t\log \log N)$ time with high probability for finding planar skyline points in a 3-sided query rectangle $q=[a,b]\times [d,+\infty )$ in the RAM model, where N is the cardinality of P and t is the answer size.

关于属性值的最小化或最大化，一组P点的天际线由“最佳”点组成。如果p在所有维度上均与q一样好，并且在至少一个维度上严格优于q，则点p将主导另一个点q。在这项工作中，我们专注于二维空间，并为动态（插入和删除）三边范围天际线查询提供预期的性能保证。我们假设这些点的x和y坐标是从一类分布中得出的，并给出了ML树（修改的分层范围树），$Ø（{\mathrm{日志}}^2ñ\mathrm{日志}\mathrm{日志}ñ）$ 预期更新时间和 $Ø（Ť\mathrm{日志}\mathrm{日志}ñ）$ 在三边查询矩形中找到平面天际线点的可能性较高的时间 $q=[\mathrm{一种}，b]\times [d，+\infty ）$在RAM模型中，其中N是P的基数，而t是答案大小。