A dynamic data structure for 3-d convex hull and 2-d nearest neighbor queries

A dynamic data structure for 3-d convex hull and 2-d nearest neighbor queries (2006)

by Timothy M. Chan

Venue:	In: Proceedings of the seventeenth ACM-SIAM symposium on Discrete algorithm
Citations:	19 - 5 self

Datum	Value	Source
TITLE	A dynamic data structure for 3-d convex hull and 2-d nearest neighbor queries	INFERENCE
AUTHOR NAME	Timothy M. Chan	SVM HeaderParse 0.2
ABSTRACT	We present a fully dynamic randomized data structure that can answer queries about the convex hull of a set of n points in three dimensions, where insertions take O(log 3 n) expected amortized time, deletions take O(log 6 n) expected amortized time, and extreme-point queries take O(log 2 n) worst-case time. This is the first method that guarantees polylogarithmic update and query cost for arbitrary sequences of insertions and deletions, and improves the previous O(n ε)-time method by Agarwal and Matouˇsek a decade ago. As a consequence, we obtain similar results for nearest neighbor queries in two dimensions and improved results for numerous fundamental geometric problems (such as levels in three dimensions and dynamic Euclidean minimum spanning trees in the plane). 1	SVM HeaderParse 0.2
YEAR	2006	INFERENCE
VENUE	In: Proceedings of the seventeenth ACM-SIAM symposium on Discrete algorithm	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	1196--1202	INFERENCE
CITATIONS	34 found	ParsCit 1.0