The C-Tree: A Dynamically Balanced Spatial Index

Abstract

We introduce an efficient and robust spatial index to support a set of different queries, which is developed from Günther’s Celltree [6] and the Monotonous Bisector* Tree [12, 17]. In practice, huge scenes are manageable by using the paging-concept. For convex polyhedrons in N-dimensional real space and any L _p -metric (1 ≤ p ≤ ∞) we are able to show that the C-tree can be constructed in time $\theta \left( {n\log n} \right)$ , linear space and logarithmic height, where n denotes the number of objects. Dynamic insertion of objects is performed in $\theta \left( {\log ^2 n} \right)$ amortized worst-case time. Objects can be deleted in amortized $\theta \left( n \right)$ (n) or in amortized $\theta \left( {\log ^2 n} \right)$ if the actualization of cluster radii can be delayed. In all cases logarithmic height and linear space requirements are preserved.