## On approximating the depth and related problems (2005)

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Venue: | In Proc. 16th ACM-SIAM Sympos. Discrete Algorithms |

Citations: | 63 - 11 self |

### BibTeX

@INPROCEEDINGS{Aronov05onapproximating,

author = {Boris Aronov and Sariel Har-peled},

title = {On approximating the depth and related problems},

booktitle = {In Proc. 16th ACM-SIAM Sympos. Discrete Algorithms},

year = {2005},

pages = {886--894}

}

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### Abstract

We study the question of finding a deepest point in an arrangement of regions, and provide a fast algorithm for this problem using random sampling, showing it sufficient to solve this problem when the deepest point is shallow. This implies, among other results, a fast algorithm for solving linear programming with violations approximately. We also use this technique to approximate the disk covering the largest number of red points, while avoiding all the blue points, given two such sets in the plane. Using similar techniques imply that approximate range counting queries have roughly the same time