Kinetic sorting and kinetic convex hulls

Let S be a set of n points moving on the real line. The kinetic sorting problem is to maintain a data structure on the set S that makes it possible to quickly generate a sorted list of the points in S, at any given time. We prove tight lower bounds for this problem, which show the following: with a subquadratic maintenance cost one cannot obtain any significant speed-up on the time needed to generate the sorted list (compared to the trivial O(n log n) time), even for linear motions. We also describe a kinetic data structure for so-called giftwrapping queries on a set S of n moving points in the plane: given a point q and a line through q such that all points from S lie on the same side of , report which point pi ∈ S is hit first when is rotated around q. Our KDS allows a tradeoff between the query time and the maintenance cost: for any Q with 1 ≤ Q ≤ n, we can achieve O(Q log n) query time with a KDS that processes O(n2+ /Q1+1/δ ) events, where δ is the maximum degree of th...

• Type: Conference
• Year: 2005
• Where: COMPGEOM
• Authors: Mohammad Ali Abam, Mark de Berg
• Keywords: COMPGEOM 2005, Convex Hull, Data Structure, Discrete Geometry, Sorted List