par Demaine, Erik D. 
;Iacono, John ;Langerman, Stefan
Référence Computational geometry, 28, 1, page (29-40)
Publication Publié, 2004-05
;Iacono, John ;Langerman, Stefan Référence Computational geometry, 28, 1, page (29-40)
Publication Publié, 2004-05
Article révisé par les pairs
| Résumé : | In the 2D point searching problem, the goal is to preprocess n points P = {p1, ..., pn} in the plane so that, for an online sequence of query points q1, ..., qm, it can quickly be determined which (if any) of the elements of P are equal to each query point q i. This problem can be solved in O(logn) time by mapping the problem to one dimension. We present a data structure that is optimized for answering queries quickly when they are geometrically close to the previous successful query. Specifically, our data structure executes queries in time O(logd(q i-1,qi)), where d is some distance function between two points, and uses O(nlogn) space. Our structure works with a variety of distance functions. In contrast, it is proved that, for some of the most intuitive distance functions d, it is impossible to obtain an O(logd(qi-1, qi)) runtime, or any bound that is o(logn). © 2004 Elsevier B.V. All rights reserved. |
