## Dynamic 3-sided Planar Range Queries with Expected Doubly Logarithmic Time

Venue: | Proceedings of ISAAC, 2009 |

Citations: | 2 - 1 self |

### BibTeX

@INPROCEEDINGS{Brodal_dynamic3-sided,

author = {Gerth Stølting Brodal and Alexis C. Kaporis and Spyros Sioutas and Kostas Tsichlas},

title = {Dynamic 3-sided Planar Range Queries with Expected Doubly Logarithmic Time},

booktitle = {Proceedings of ISAAC, 2009},

year = {}

}

### OpenURL

### Abstract

Abstract. We consider the problem of maintaining dynamically a set of points in the plane and supporting range queries of the type [a, b] × (−∞, c]. We assume that the inserted points have their x-coordinates drawn from a class of smooth distributions, whereas the y-coordinates are arbitrarily distributed. The points to be deleted are selected uniformly at random among the inserted points. For the RAM model, we present a linear space data structure that supports queries in O(log log n + t) expected time with high probability and updates in O(log log n) expected amortized time, where n is the number of points stored and t is the size of the output of the query. For the I/O model we support queries in O(log log B n + t/B) expected I/Os with high probability and updates in O(log B log n) expected amortized I/Os using linear space, where B is the disk block size. The data structures are deterministic and the expectation is with respect to the input distribution. 1