## In-Place 2-d Nearest Neighbor Search (2007)

by
Timothy M. Chan
,
Eric Y. Chen

Citations: | 1 - 1 self |

### BibTeX

@MISC{Chan07in-place2-d,

author = {Timothy M. Chan and Eric Y. Chen},

title = {In-Place 2-d Nearest Neighbor Search},

year = {2007}

}

### OpenURL

### Abstract

Abstract We revisit a classic problem in computational geometry: preprocessing a planar n-point set to answer nearest neighbor queries. In SoCG 2004, Br"onnimann, Chan, and Chen showed that it is possible to design an efficient data structure that takes no extra space at all other than the input array holding a permutation of the points. The best query time known for such "in-place data structures " is O(log 2 n). In this paper, we break the O(log 2 n) barrier by providing a method that answers nearest neighbor queries in time O((log n) log3=2 2 log log n) = O(log