Dynamic Point Location in General Subdivisions

Hanna Baumgarten, Hermann Jung, Kurt Mehlhorn

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 S segments; •Delete(s segment): Remove segment s from the collection S of segments. We present a solution which requires space O(n), has query and insertion time O(log n loglog n) and deletion time O(log2 n). A query time below O(log2 n) was previously only known for monotone subdivisions and horizontal segments and required non-linear space.