Although constructing the convex layers by repeatedly finding convex hulls would be slower, it is possible to partition any set of <math>n</math> points into its convex layers in time <math>O(n\log n)</math>.<ref name="c85"/>
Convex layers may be used as part of an efficient [[range searchreporting]] data structure for listing all of the points in a query [[half-plane]]. The points in the half-plane from each successive layer may be found by a binary search to find the most extreme point in the direction of the half-plane, and then searching sequentially from there. [[Fractional cascading]] can be used to speed up the binary searches, giving total query time <math>O(\log n+k)</math> to find <math>k</math> points out of a set of <math>n</math>.<ref name="c85"/>
