ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Indexing non-uniform spatial data
IDEAS'97 Proceedings of the 1997 international conference on International database engineering and applications symposium
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We consider the problem of dynamic range searching in tree structures that do not replicate data. We propose a new dynamic structure, called the {\em O-tree\/}, that achieves a query time complexity of $O(n^{(d-1)/d})$ on $n$ $d$-dimensional points and an amortized insertion/deletion time complexity of $O(\log n)$. We show that this structur e is optimal when data is not replicated. In addition to optimal query and insertion/deletion times, the O-tree also supports exact match queries in worst-case logarithmic time.