## I/O-efficient dynamic planar point location.(English)Zbl 1056.68062

Summary: We present an I/O-efficient dynamic data structure for point location in a general planar subdivision. Our structure uses $$O(N/B)$$ disk blocks of size $$B$$ to store a subdivision of size $$N$$. Queries can be answered in $$O(\log^2_BN)$$ I/Os in the worst case, and insertions and deletions can be performed in $$O(\log^2_BN)$$ and $$O(\log_BN)$$ I/Os amortized, respectively.
Part of our data structure is based on an external version of the so-called logarithmic method that allows for efficient dynamization of static external-memory data structures with certain characteristics. Another important part of our structure is an external data structure for vertical ray-shooting among line segments in the plane with endpoints on $$\sqrt B+1$$ vertical lines, developed using an external version of dynamic fractional cascading. We believe that these methods could prove helpful in the development of other dynamic external memory data structures.

### MSC:

 68P05 Data structures

### Keywords:

dynamic data structure; logarithmic method
Full Text:

### References:

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