Point Location in Dynamic Planar Subdivisions

We study the point location problem on dynamic planar subdivisions that allows insertions and deletions of edges. In our problem, the underlying graph of a subdivision is not necessarily connected. We present a data structure of linear size for such a dynamic planar subdivision that supports sublinear-time update and polylogarithmic-time query. Precisely, the amortized update time is O(sqrt{n}log n(log log n)^{3/2}) and the query time is O(log n(log log n)^2), where n is the number of edges in the subdivision. This answers a question posed by Snoeyink in the Handbook of Computational Geometry. When only deletions of edges are allowed, the update time and query time are just O(alpha(n)) and O(log n), respectively

A Fully Dynamic Planar Point Location Technique

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryNational Science Foundation / ECS 84-1090

A Dynamic Data Structure for Planar Graph Embedding

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryNational Science Foundation / ECS-84-1090