アイテム詳細

要旨

We give an algorithm that maintains an approximation of the width of a set of $n$ points in the plane in $O(\alpha\log n)$ amortized time, if only insertions or only deletions are performed. The data structure allows for reporting the approximation in $O(\alpha\log n\log\log n)$ time. $\alpha$ is a parameter that expresses the quality of the approximation. Our data structure is based on a method of Janardan that maintains an approximation of the width under insertions and deletions using $O(\alpha\log^2 n)$ time for the width query and the updates.