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Abstract:
In this paper, we consider dynamic data structures for order
decomposable problems. This class of problems include the convex hull
problem, the Voronoi diagram problem, the maxima problem,
and intersection of halfspaces.
This paper first describes a scheme for maintaining convex hulls in
the plane dynamically in $O(\log n)$ amortized time for insertions and
$O(\log^2 n)$ time for deletions. $O(n)$ space is used.
The scheme improves on the time complexity of the general scheme
by Overmars and Van Leeuwen. We then consider the general class
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 {\em change sensitive}, i.e., updates to the solution
of the problem at an insertion can be obtained in time proportional
to the changes.
