Optimal Dynamic Range Searching inNon-replicating Index Structures

  • K. V. Ravi Kanth
  • Ambuj Singh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1540)

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • K. V. Ravi Kanth
    • 1
  • Ambuj Singh
    • 2
  1. 1.Oracle NEDCNashuaUSA
  2. 2.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA

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