Lecture Notes: External Interval Tree
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چکیده
We leave the proof to you. Both the space and query complexities are known to be optimal (the optimality proof requires knowledge about some sophisticated lower bounds in the cell probe model, and is beyond the scope of this course). We will focus on the dynamic setting of the problem, where the structure needs to support insertions and deletions, and yet, still answer queries efficiently. The persistent B-tree falls short for this purpose. We will discuss an alternative structure called the external interval tree designed by Arge and Vitter [1]. The structure uses linear space, answers a query in O(logB N+K/B) I/Os, and supports an update (both insertion and deletion) in O(logB N) I/Os. For simplicity, we assume that the intervals in I are in general position, such that all the (left and right) endpoints in I are distinct. Also, we make the tall cache assumption that M ≥ B.
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تاریخ انتشار 2014