ISSN:
1432-0444
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract Given a fixed setS ofn points inE 3 and a query planeπ, the halfspace range search problem asks for the retrieval of all points ofS on a chosen side ofπ. We prove that withO(n(logn)8 (loglogn)4) storage it is possible to solve this problem inO(k+logn) time, wherek is the number of points to be reported. This result rests crucially on a new combinatorial derivation. We show that the total number ofj-sets (j=1, ...,k) realized by a set ofn points inE 3 isO(nk 5); ak-set is any subset ofS of sizek which can be separated from the rest ofS by a plane.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02187685