Dynamic Planar Convex Hull with Optimal Query Time

Dynamic Planar Convex Hull with Optimal Query Time and O(log n log log n) Update Time

Dynamic Planar Convex Hull with Optimal Query Time and O ( log n · log log n ) Update Time Gerth

The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log logn) time, point deletions in amortized O(log n · log logn) time, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure requi...

Convex Hull with Optimal Query Time and O ( log n · log log n ) Update Time

The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log logn) time, point deletions in amortized O(log n · log logn) time, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure requi...

On the convex layers of a planar set

Let S be a set of n points in the Euclidean plane. The convex layers of S are the convex polygons obtained by iterating on the following procedure: compute the convex hull of S and remove its vertices from S. This process of peeling a planar point set is central in the study of robust estimators in statistics. It also provides valuable information on the morphology of a set of sites and has pro...

Planar Convex Hull Range Query and Related Problems

We consider the planar convex hull range query problem. Let P be a set of points in the plane. We preprocess these points into a data structure such that given an orthogonal range query, we can report the convex hull of the points in the range in O(log n + h) time, where h is the size of the output. The data structure uses O(n log n) space. This improves the previous bound of O(log n+h) time an...