In this paper, we examine the complexity of multi-dimensional range searching in non-replicating index structures. Such non-replicating 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.
CITATION STYLE
Kanth, K. V. R., & Singh, A. (1998). Optimal dynamic range searching in non-replicating index structures. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1540, pp. 257–276). Springer Verlag. https://doi.org/10.1007/3-540-49257-7_17
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