Abstract
In this paper, we examine the complexity of multi-dimensional range searching in non-replicating index structures. Such nonreplicating structures achieve low storage costs and fast update times due to lack of multiple copies. We first obtain a lower bound for range searching in non-replicating structures. Assuming a simple tree structure model of an index, we prove that the worst-case time for a query retrieving t out of n data items is Ω(n/b)(d-1)/d + t/b), where d is the data dimensionality and b is the capacity of index nodes. We then propose a new index structure, called the O-tree, that achieves this query time in dynamic environments. Updates are supported in O(logb n) amortized time and exact match queries in O(logb n) worst-case time. This structure improves the query time of the best known non-replicating structure, the divided k-d tree, and is optimal for both queries and updates in non-replicating tree structures.
Work supported in part by research grants NSF/ARPA/NASA IRI-9411330 and NSF CCR-9505807.
Work done when the author was at University of California, Santa Barbara
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Ravi Kanth, K.V., Singh, A. (1999). Optimal Dynamic Range Searching inNon-replicating Index Structures. In: Beeri, C., Buneman, P. (eds) Database Theory — ICDT’99. ICDT 1999. Lecture Notes in Computer Science, vol 1540. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49257-7_17
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