Dynamic point location in general subdivisions

Abstract

The dynamic planar point location problem is the task of maintaining a dynamic set S of n non-intersecting, except possibly at endpoints, line segments in the plane under the following operations: Locate (q: point): Report the segment immediately above q, i.e., the first segment intersected by an upward vertical ray starting at q; Insert (s: segment): Add segment s to the collection of S of segments; Delete (s: segment): Remove segment s from the collectection S of segments. We present a solution which requires space O(n), has query and insertion time O(log n log log n) and deletion time O(log"2n). A query below O(log"2n) was previously only known for monotone subdivisions and horizontal segments and required non-linear space. (orig.)SIGLEAvailable from TIB Hannover: RR 2036(16) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman