Hulls and Order Decomposable Problems

In this paper we consider dynamic data structures for Order Decomposable Problems. This dass of Problems indude the Convex Hull Problem, the Voronoi Diagram Problem, the Maxima Problem and the Intersection of Half Spaces. This paper first describes a scheme for maintaining convex hulls in the plane dynamically in O(logn) amortized time for insert ions and O(log2n ) time for deletions. O(n) space is used. The scheme improves on the time complexity of the original scheme by Overmars and Van Leeuven. We then consider the general dass of Order Decomposable Problems. We show improved behavior for insertions in the presence of deletions, under some assumptions. The main assumption we make is that the problems are required to be change sensitive, Le. updates to the solution of the problem at an insertion can be obtained in time proportional to the changes.